University of Denver
Digital Commons @ DU
Electronic Theses and Dissertations
Graduate Studies
1-1-2016
Modeling and Simulation of Optical Properties of
Noble Metals Triangular Nanonprisms
Soad Zahir Alsheheri
University of Denver, [email protected]
Follow this and additional works at: http://digitalcommons.du.edu/etd
Recommended Citation
Alsheheri, Soad Zahir, "Modeling and Simulation of Optical Properties of Noble Metals Triangular Nanonprisms" (2016). Electronic
Theses and Dissertations. 1107.
http://digitalcommons.du.edu/etd/1107
This Dissertation is brought to you for free and open access by the Graduate Studies at Digital Commons @ DU. It has been accepted for inclusion in
Electronic Theses and Dissertations by an authorized administrator of Digital Commons @ DU. For more information, please contact
[email protected].
MODELING AND SIMULATION OF OPTICAL PROPERTIES OF NOBLE METALS
TRIANGULAR NANOPRISMS
__________
A Dissertation
Presented to
the Faculty of the Daniel Felix Ritchie School of Engineering and Computer Science
University of Denver
__________
In Partial Fulfillment
of the Requirements for the Degree
Doctor of Philosophy
__________
by
Soad Alsheheri
June 2016
Advisor: Mohammad Matin
Author: Soad Alsheheri
Title: MODELING AND SIMULATION OF OPTICAL PROPERTIES OF NOBLE
METALS TRIANGULAR NANOPRISMS
Advisor: Mohammad Matin
Degree Date: June 2016
Abstract
Gold and silver has gained huge attention across the scientific community for its
applications arising from its plasmonic properties. The optical properties achieved by
these materials via excitation of plasmons is very unique to these materials and used as
diagnostic and therapeutic agents in the field of medicine, and as sensors in a gamut of
disciplines such as energy and environmental protection to name a few. Surface plasmon
resonance (SPR) properties of the gold and silver are size and shape dependent. Of the
various shapes reported in literature, triangular nanoprisms has tunable optical properties
in the visible and near IR region by manipulating the structural features such as thickness,
edge length, and morphology of tip. To understand the effect of these parameters on
dipole surface plasmon resonance we have constructed triangular silver nanoprism and
sandwich of gold and triangular nanoprism using Optiwave FDTD. Silver triangular
nanoprism has exhibited blue shift on introduction of truncation and the blue shift
continued further with depth of truncation. Similar observations were made for increase
in thickness of nanoprism. In contrast, increase in edge length of the nanoprism has
introduced a blue shift in dipole surface plasmon resonance. Coupling of gold and silver
as sandwich with a dielectric material has introduced two plasmon resonance peaks in the
ii
visible and near IR region. In contrast to individual silver triangular nanoprism,
increasing the edge length and thickness of gold and silver has introduced a red shift.
Interestingly, thickness of the dielectric layer controls the wavelength of the dipole
plasmon resonance of metals in the sandwich and its strength.
iii
Acknowledgements
In acknowledgment of the personal and professional support I have received
throughout the process of completing my Ph.D. study, I would like to begin by
expressing my deep gratitude to Professor Mohammad Matin, my advisor. He has
provided, with unfailing patience and kindness, the continuous guidance that has
motivated my research and writing.
Sincere thanks are also due to the rest of my dissertation committee: Prof.
Matthew Gordon, Prof. Yun-Bo Yi, and Dr. Vi Narapareddy, for maintaining their
encouragement and support throughout the process. With comments and hard questions
from their various perspectives, they have given me the inspiration to widen my research.
For my initial enlightenment and first glance at attempting the research, I offer my
sincere thanks to Dr. Marjan Saboktakin. She has been a wonderful friend who has
willingly given of her time and immense knowledge to provide me with the motivation to
complete the research process.
I would also like to thank my family, my parents, my brothers, and my sisters, for
supporting and encouraging me with their best wishes. A special word of thanks goes to
my lovely son Mazen.
With special love and gratitude, my final thanks go to my husband, without whose
support, patience, and sacrifice, I could not have completed this dissertation.
iv
Table of Contents
Abstract ............................................................................................................................... ii
Acknowledgements ............................................................................................................ iv
List of Figures .................................................................................................................. viii
List of Table ....................................................................................................................... xi
Chapter One: Introduction .................................................................................................. 1
1.1 Background ....................................................................................................... 1
1.2 Problem Statement ............................................................................................ 2
1.3 Objective ........................................................................................................... 3
1.4 Scope of Research Work ................................................................................... 3
1.5 Methodology ..................................................................................................... 4
1.6 Contribution and Publications........................................................................... 4
1.7 Chapter Organization ........................................................................................ 5
Chapter Two: Sutface Plasmon Resonances (SPRs) .......................................................... 7
2.1 Introducion ........................................................................................................ 7
2.2 Mie Theory...................................................................................................... 16
2.3 Postulates of Mie Theory ................................................................................ 16
2.4 Deviation from Sphericity............................................................................... 17
2.5 Limitation of Mie Theory ............................................................................... 17
2.6 Effective Medium Theory ............................................................................... 17
2.7 Discrete Dipole Approximation Method ........................................................ 25
2.8 Finite Difference Time-Domain Method (FDTD) .......................................... 28
2.8.1 One-Dimensional Simulation........................................................... 32
2.8.2 Two-Dimensional Simulations ........................................................ 34
2.8.3 Three-Dimensional Simulation ........................................................ 35
2.9 FDTD Simulation Software ............................................................................ 37
2.10 Lorentz-Drude Model (FDTD) ..................................................................... 39
2.11 Anisotropic Colloidal Assemblies ................................................................ 41
2.11.1 Effect of Snipping or Truncation ................................................... 44
2.11.2 Effect of dielectric on plasmonic properties .................................. 44
2.12 Synthesis of Nanomaterials........................................................................... 45
2.13 Synthesis of Triangular Nanoprisms ............................................................. 47
2.14 FDTD Simulation Parameters ....................................................................... 64
Chapter Three: Study of the Snip Effect in Resonance of Gold and Silver Triangular
Nanoprisms ....................................................................................................................... 68
3.1. The effect of the edge length and thickness of perfect triangular gold and
silver nanoprism .................................................................................................... 68
v
3.2 The effect of edge length and thickness of truncated triangular gold and silver
nanoprism .............................................................................................................. 72
3.3 The effect of truncation of gold and silver...................................................... 85
3.4 Conclusion ...................................................................................................... 97
Chapter Four: The Effect of Truncation and Dielectric in Plasmonic Resonance of
Hybrid Plasmonic Nanosandwich Structures in Optical Range ....................................... 98
4.1 Introduction ..................................................................................................... 98
4.2 The Effect of Dielectric ................................................................................ 100
4.3 Ag- dielectric-Au Sandwich ......................................................................... 110
4.4 Conclusion .................................................................................................... 116
Chapter Five: Summary & Future Work ........................................................................ 117
References ....................................................................................................................... 119
Appendix A: A List od Publication. ............................................................................... 141
vi
List of Figures
Figure 2.1 Size dependent colors of gold nanoparticles ..................................................... 8
Figure 2.2 Scheme depicting relationship between number of atoms exposed to surface to
the total number of atoms in volume .................................................................................. 9
Figure 2.3: Interaction between electromagnetic radiation and surface electrons.
Reproduced from reference............................................................................................... 11
Figure 2.4: Three magnetic fields originating from the common node ............................ 30
Figure 2.5 The geometry of the spherical dielectric target ............................................... 31
Figure 2.6 Schematic representation of experimental set-up for preparation of
nanoparticles via inert-gas condensation method ............................................................. 47
Figure 2.7 Synthesis of triangular gold nanoprisms along with some spherical
nanoparticles ..................................................................................................................... 48
Figure 2.8 Scanning electron microscopy images of gold nanoprisms with various
dimensions synthesized using PVP to HAuCl4 ratio ........................................................ 49
Figure 2.9 synthesis of triangular nanoplates after evaporation of solvent as seen in TEM
........................................................................................................................................... 59
Figure 2.10 pH controlled synthesis of silver triangular nanoprisms at irradiation
wavelength of 550 nm at pH 11.2 ..................................................................................... 62
Figure 3.1 Effect of edge length on plasmon resonance for triangular nanoprisms of a)
Ag b) Au ........................................................................................................................... 75
Figure 3.2 Effect of thickness on plasmon resonance for triangular nanoprism of (a) Ag
(b) Au ................................................................................................................................ 79
Figure 3.3 Effect of edge length on plasmon resonance for truncated triangular
nanoprisms of a) Ag b) Au............................................................................................... 81
Figure 3.4 Effect of thickness of nanoprism on plasmon resonance for truncated
triangular nanoprisms of a) Ag b) Au .............................................................................. 82
Figure 3. 5: Comparison of effect of edgelength on dipole plasmon resonance of perfect
and truncated nanoprisms of a) Ag b) Au ......................................................................... 83
Figure 3. 6: Comparison of effect of thickness on dipole plasmon resonance of perfect
and truncated nanoprisms of a) Ag b) Au ......................................................................... 84
Figure 3.7. Comparison of Ag and Au triangular nanoprisms for change in dipole
plasmon resonance with variation in degree of truncation. .............................................. 87
Figure 3.8. Effect of degree of truncation at only one vertex of Ag nanoprism on dipole
plasmon resonance. ........................................................................................................... 89
Figure 3.9. Plasmonic resonance of triangular Ag nanoprisms with truncation in one,
two, and three vertices (A) wavelength position of the peaks. (B) absorbance strength of
the peaks............................................................................................................................ 90
vii
Figure 3.10 FDTD simulation results showing the plasmonic resonance of nanoprism that
has thickness of 30 nm and edge length of 100 nm with different degrees of truncation
for (A) Ag. (B) Au. ......................................................................................................... 93
Figure 3.11 The plasmonic enhancement of Ag nanoprism without snipping (a and b) and
truncated nanoprism (c and d) with snip of 10 nm. The edge length (100 nm) and
thickness (30nm) were maintained constant in above figure (a – d). ............................... 95
Figure 3.12 The plasmonic enhancement of Au nanoprism without snipping (a and b) and
truncated nanoprism (c and d) with snip of 10 nm. The edge length (100 nm) and
thickness (30nm) were maintained constant in above figure (a – d). ............................... 96
Figure 4.1 FDTD simulation results showing the absorbance spectra of Ag nanosandwich
structures with edge length of 100 nm and thickness 30 nm. This figure of for dielectric
thickness of 50 nm. ......................................................................................................... 104
Figure 4.2 FDTD simulation results showing the absorbance spectra of Au nanosandwich
structures with edge length of 100 nm and thickness 30 nm. This figure of for dielectric
thickness of 50 nm. ....................................................................................................... 105
Figure 4.3: Effect of refractive index on dipole plasmon resonance maximum for various
thicknesses of dielectric of a) Ag b) Au.......................................................................... 106
Figure 4.4: Comparison of dipole resonance maximum for Ag and Au towards change in
dielectric medium with thickness of 30 nm .................................................................... 107
Figure 4.5. FDTD Simulation results showing the plasmonic resonance of Au and Ag
nanoprism with edge length of 100 nm and thickness of 30 nm and FDTD Simulation
results showing the plasmonic resonance of an Au- dielectric-Ag nanoprism with edge
length of 100 nm and thickness of 30 nm for all layers. (solid black line), ( A: edge
length, B: height, and C: thickness) ................................................................................ 108
Figure 4.6 (a) FDTD simulation results showing the absorbance of sandwich structure
(Au/dielectric/Ag) (a) without truncation and (b) with TR= 0.1 (First peak is
corresponding to Au & Second peak is corresponding to Ag). ...................................... 114
Figure 4.7: Relationship between the magnitude of Ag and Au peaks and varying
thickness of dielectric layer (nm) (A) Perfect sandwich structure and (B) Truncated
sandwich structure. ......................................................................................................... 115
viii
List of Tables
Table 3.1: Effect of edge length on dipole plasmon resonance of triangular nanoprisms of
Ag and Au truncated and non-truncated ........................................................................... 78
Table 3.2: Effect of edge length on dipole plasmon resonance of triangular nanoprisms of
Ag and Au truncated and non-truncated ........................................................................... 78
Table 3.3: Effect of truncation on dipole plasmon resonance of triangular nanoprisms of
Ag and Au ......................................................................................................................... 92
Table 3.4: Full Width Half Maximum of dipole plasmon resonance of truncated
triangular nanoprisms of Ag and Au ................................................................................. 92
Table 4.1: Summary of results investigated for effect of dielectric thickness for various
refractive indices on dipole plasmon resonance ............................................................. 101
Table 4.2: Summary of results investigated for effect of dielectric thickness for various
refractive indices on dipole plasmon resonance ............................................................. 101
ix
Chapter 1
Introduction
1.1 Background
Optical sensors that operates via the generation of surface plasmons are typically
known as surface plasmon resonance sensors. These optical sensors has gained huge
interest in the sensing technology for the detection of analytes ranging from chemicals,
biological species, environmental regulation, medical diagnostic applications etc. [1]–[5]
These surface plasmon resonance based optical sensors utilize various methods of optical
excitation such as attenuated total reflection and grating coupling. Typical modulation
methodologies are based on surface plasmons in wavelength [6], [7] and angular domains
[8], [9]. In the broad field of sensing technology Au and Ag have received great attention
due to its unique optical properties, in particular optical enhancement [10]. The optical
enhancement in noble metal nanoparticles particularly in Ag and Au ensues from
resonant coupling of metals conduction electrons with incident electromagnetic radiation
and through strong scattering in nano-dimensions [11], [12]. Both, resonant coupling of
metal conduction electrons with incident light and scattering process has its own
applications. Scattering process leads applications in diagnostics [13], [14] through
imaging and therapeutic applications through thermal dissipation process leading to
1
localized heat from the absorbed light [15], [16]. When gold and silver are employed for
applications in sensors, the changes in absorption or scattering of plasmonic resonance
will be measured with respect to change in chemical and physical environment of
nanoparticle surface.
Conventional biological sensors employs labels to create and augment the target
signal. Labels are depending on applications, it can range from fluorophores, enzymes or
radioisotopes to name a few. While the labeling methods is useful to measure signals, for
studies involving understanding of biomolecules in its real-time environment are
impossible with techniques that employs labels affects the biological interactions. Thus
label free techniques are preferred. Additionally, presence of labels enables sensing
through end-points assays only. Considering those disadvantages, it is label free surface
plasmon resonance sensing is the most desired technique [17]. The prime disadvantage
with label free sensing is low sensitivity. However the low sensitivity issue can be
addressed through manipulation of metal nanoparticles such as size, geometry and
composition [18]–[20].
1.2 Problem Statement
Although silver and gold has interesting optical properties, its potentials in
plasmonic properties has been extensively investigated only as spherical particles.
Further when gold and silver in spherical form offers limited opportunity to tune optical
properties through variation in structure. It is desired at this moment, we need better ways
to tune these materials for various sensing applications in visible and near infra-red
2
region. This objective can be achieved through changing the morphology of gold and
silver nanoparticles from conventional spherical particles. Particularly, we believe, gold
and silver has a lot to offer when they are in the form of triangular nanoprism.
1.3 Objective
The objective of our research work is, how to tune the surface plasmonic
properties for various applications that uses sensors. We have discussed the advantages of
triangular nanoprisms and its applications available in literature. Then, we propose here
that gold and silver triangular nanoprism can offer the opportunity to tune the plasmonic
properties through manipulation of dimensions.
1.4 Scope of Research Work
In this dissertation we mainly focused on identifying the advantages of gold and
silver when present in the form of triangular nanoprisms to plasmonic properties. In
chapter 2 we have investigated the effect of dimensions of triangular nanoprism i.e., edge
length and thickness and how it can be tuned to various sensing application in infra-red
region and visible region. In chapter we studied the effect of truncation and advantages of
constructing a triangular nanoprism that couples dielectric, silver and gold. The studies
presented in chapter 2 and chapter shed light on tunability of plasmonic properties by
manipulating the dimensions of nanoprism and composition of nanoprism.
3
1.5 Methodology
To achieve our objectives we have used Opti-FDTD simulation software. This
powerful tool was used to understand the dependence of plasmonic properties of
triangular nanoprisms of gold and silver nanoparticles through simulations.
1.6 Contribution and Publications
This research is about the study of plasmonic properties of triangular nanoprisms.
All of the research presented in this dissertation were submitted to peer reviewed
journals. Following paragraphs will briefly summarize the content we presented for
publication:
We studied the effect of truncation on the plasmonic resonance of triangular
nanoprisms. Perfect Ag triangular prisms and Ag truncated triangular prisms have been
designed and simulated using finite-difference time-domain (FDTD) simulation
technique. Simulation results show that the increase of the truncations depth in triangular
nanoprisms causes a resonance blue shift. However, for the case of truncation depth of up
to 15 nm, the number of truncated corners has no effect on the position of the peak or the
strength.
Hybrid plasmonic nanoprisms with and without truncation in the form of gold
(Au)-dielectric- silver (Ag) sandwich nano-structures have been designed and simulated
using Finite-difference time-domain (FDTD) simulation technique. Simulations results
show two dipole resonant peaks for the hybrid sandwich structure. Also, a strong
wavelength dependence of the plasmonic resonance peaks on the edge length and the
4
thickness of gold and silver layers. The increase in edge length and the decrease in
thicknesses were found to cause red shift to the plasmonic peak of the nanostructures.
Moreover, the full width half maximum (FWHM) of the truncated nanoprism
sandwich structure is smaller than (FWHM) for nanoprism sandwich structure without
truncation. Furthermore, the resonant wavelengths and relative strength of the two-dipole
plasmonic peaks are demonstrated to be tunable.
1.7 Chapter Organization
This dissertation constitutes four chapters. The layout of the chapters are as
follows:
Chapter 1 includes brief background, problem statement, objective, scope and
implications of the research, methods used to perform the research and finally chapter
organization.
Chapter 2 offers a brief history of gold and silver in ancient days followed by
discussion about importance and introduction of noble metal nanoparticles in various
fields in modern days. Origin of surface plasmon resonance, role of silver and gold in
plasmonic properties, size and shape dependent properties of silver and gold on
plasmonic properties were discussed. Methodology (Finite Difference Time Domain)
used to measure the plasmonic properties of gold and silver were discussed briefly.
Chapter 3 covers the construction of gold and silver triangular nanoprism using
Opti-FDTD software. The dimensions of triangular nanoprism such as edge length and
thickness and its impact on plasmonic properties were investigated. Followed by, effect
5
of truncation in plasmonic properties were also analyzed thoroughly and compared the
results with perfect triangular nanoprisms of gold and silver.
Chapter 4 investigates the role of dielectric and its thickness on plasmonic
properties of gold and silver individually. Additionally, we constructed a triangular
nanosandwich prism made up of gold, silver and dielectric and analyzed for tunability of
surface plasmon resonance. Effect of thickness of dielectric in truncated and perfect
nanosandwich were also thoroughly studied.
6
Chapter 2
Surface Plasmon Resonances (SPRs)
2.1 Introduction
Gold and Silver has been the premises of exploration since the ancient days [21].
Early civilizations used these materials as medicines, utensils, plates, cups, jewelry,
coins, clothes, construction materials and as disinfectant for human and water borne
infections [22]. From age-old time, these metals have been part of our civilizations. Until
a century ago, applications of gold and silver were primarily focused on medicinal based
applications [23]–[27]. Apart from medicinal based applications, silver was explored as
catalyst for reactions such as methanol to formaldehyde and ethylene oxide from ethene.
Much of the applications mentioned above, based on macroscopic properties of the noble
metals.
Non macroscopic properties of noble metals dates back to several centuries in the
form of Lycurgus cup which exhibits ruby red in transmitted light and in reflected light it
is green in color. Faraday offered the explanation for colors in Lycurgus cup was due to
colloidal nature of gold particles whose interactions with light are different from bulk
gold [28]. French dictionary in 18th century reported “drinkable gold” that had different
7
colors, (Figure 1.1) where gold is in its elementary form under extreme sub-division
which is not visible to human eye [29]. Benjamin Richters explained, purple or pink
colors of drinkable gold by variation in synthesis procedures [30]. Yellow color of the
gold solution is observed when the gold particles are aggregated due to reduction in
reflectivity for light towards the end of the spectrum [31]. Mie was the first one to offer
scientific explanation of colors of gold based on its size dependence [32], [33]. The
explanation offered by Mie based on phenomenon called “Surface Plasmon Resonance”
[34]. Further momentum was gained to investigate the noble metal properties that
depends on size came from famous lecture “There's Plenty of Room at the Bottom” by
Richard Feynman and opened new era of materials called nanomaterials [35]. These
nanomaterials are foundation of today’s nanoscience and nanotechnology which
encompasses a broad range of interdisciplinary areas of research and transforming the
ways in which materials and products are synthesized and the variety and nature of
functionalities that can be derived.
Figure 2.1: Size dependent colors of gold nanoparticles [36].
8
Nanomaterials are defined as materials that have at least one dimension in the
range of 1 to 100 nanometer (nm) [37], [38]. These materials at this scale possess unique
opto- electronic, magnetic and mechanical properties [40].
Figure 2.2: Scheme depicting relationship between number of atoms exposed to surface
to the total number of atoms in volume [39].
The unique properties of nanomaterials arise from greater surface area to volume
ratio [41], [42], high surface energy, spatial confinement and new quantum effects [43].
At macroscopic scale, i.e., in millimeter scale, the number of atoms exposed to surface is
typically in negligible proportions compared to total number of atoms in the bulk
material. Hence the surface atoms does not affect the bulk properties. However, in nanodimension, the proportion of atoms exposed to surface, cannot be ignored. To put this in
9
perspective, for an object of 5 nm size, about 20% of atoms are exposed to the surface,
however for nanomaterial at 2 nm dimension, roughly 50 % of atoms are exposed in the
surface. The empirical relationship between the numbers of atoms exposed to surface
(Ns) to total number of atoms in the volume Nv is given by the equation (1). This can be
expressed in a scheme as shown in Figure 1.
……………..(1)
Nanomaterials are classified as zero dimensional (spheres and clusters), one
dimensional (nanofibers), two-dimensional (2D films, plates and networks) and threedimensional (nanoprisms, tripods, cubes) materials. These nanomaterials are synthesized
by two approaches: a) top down – break or dissociate bulk materials into finer units until
it attains nano-dimensions b) bottom-up – assembling atoms or molecules into
nanostructured arrays [44]. Using one of the above mentioned strategies, the methods
adopted to synthesize nanomaterials are mechanical grinding, sol-gel process, chemical
vapor deposition, flame assisted ultrasonic spray pyrolysis, gas condensation processing,
sputtered plasma processing, microwave plasma processing and laser ablation to name a
few. Noble metal nanoparticles has been in limelight light since the concept of
nanomaterials were evolved. The reason behind the center of attraction of silver and gold
are due to applications in various genres of science and technology [45]–[53]. Of the
several choices of metal nanoparticles, noble metal nanoparticles especially gold and
silver unveils a intense absorption band in the visible region owing to its small particle
10
effect which is not seen either in bulk nor in individual atom [54]. The absorption of light
by metal nanoparticles arises from the coherent oscillation of electrons from conduction
band when induced by electromagnetic radiation (Figure 2.3).
Figure 2.3: Interaction between electromagnetic radiation and surface electrons.
Reproduced from reference [55]
The propagation of electromagnetic surface waves between conducting and
dielectric materials over a broad range of frequencies extending from dc and radio
frequencies up until the visible region. The coupling of electromagnetic field to
oscillations of conduction electrons are defined as surface plasmons. The surface are very
sensitive to the properties of the materials on which they propagate. The surface
plasmons are characterized by strong field augmentation at the interface while electric
field decays exponentially away from the surface [56]–[59]
If the dimensions of
conductor are in nano-dimensions, boundary and surface effects becomes very
11
significant, thus, the optical properties of metal nanoparticles are dominated by collective
oscillation of conduction electrons [60], [61].
When the oscillation of conduction
electrons are in resonant with frequency of incident photons are defined as surface
plasmon resonance (SPR) [56], [57], [62].
It was in 1902, surface plasmon resonance was first observed by Wood [63]. He
observed this phenomenon as an anomaly on a spectrum collected for light diffraction
through a metallic diffraction grating. Later Fano accounted for anomalies observed by
Wood as they were arising from excitation of surface electromagnetic waves with
diffraction grating of the metal [64]. First demonstration of surface plasmon resonance
through drop in reflectivity via attenuated total reflectance was given by Otto [65].
Similar observations through attenuated total reflectance were made by Raether and
Kretschmann supporting the Otto’s demonstration [66].
These groundbreaking
observations, lead path to easy ways to create surface plasmons was developed through
intense research in this field and eventually leading this phenomenon found its way into
modern optics. Several reviews and books were published periodically in understanding
the fundamentals of the surface plasmons [57], [58], [67]–[69].
For most common metals such as lead, tin, cadmium and indium the SPR
frequency occurs in the ultraviolet region of the spectrum and hence it does not exhibit
strong color effects. Further, these metals are readily oxidized under surface plasmon
resonant conditions or atmospheric conditions. Contrary to common metals, the coinage
metals under atmospheric conditions form stable colloids and have d-d transitions in the
12
visible spectrum. Additionally, imaginary part of the dielectric constant is too small
hence, near-field effect is very high which makes plasmon excitation very interesting in
noble metals. The surface plasmon resonance frequency is strongly dependent on
dielectric properties, local environment, size, shape and interparticle interactions [70]–
[75]. The oscillation frequency of nanoparticles depends on electron density, effective
electron mass, shape and size of charge distribution. Particularly, plasmonic research is
very exclusive to the gold and silver nanoparticles than most coinage metals due to high
density of conduction electrons in these materials enables plasmon resonances at optical
frequencies. High conduction electrons density enhances the electrostatic restoring force
which in turn enhances the plasmon resonance frequency. Another factor which really
distinguishes silver and gold from rest of the coinage metals is the plasmon losses. The
plasmon losses or dissipation for gold and silver is very small when compared other
coinage metals. In fact, between gold and silver, silver has the strong plasmon resonance
due to least plasmon dissipation. Despite the strong plasmon resonance exhibition by
silver, gold is more often used owing to its chemical and physical stability.
The electromagnetic radiation incident on nanoparticle induces a polarization of
free electrons on the metal surface. During the polarization, the positive charges on the
nanoparticles are immobile, whereas the electrons are in motion under the stimulus of
external field which causes the separation of negative charges from the positive charges.
Thus a net charge separation occurs at the nanoparticles boundaries. A consequence of
this charge separation ensues a linear restoring force to the system, resulting in formation
13
of dipolar oscillation. Such formed dipolar oscillation are known as dipole plasmon
resonance. The dipole plasmon resonance is different from plasmon excitations that
originates from bulk metal surface. In surface plasmon resonance, the free electrons in
the conduction band are excited in a coherent fashion that leads to in-phase oscillation
[76]. Plasmons can occur in bulk as well as at the surface of the big lumps of the
materials too [77], [78]. Due to mismatch in plasmon dispersion and photon of incident
light in bigger particles, ordinary plane of light cannot excite the plasmons. Interestingly,
in small particles plasmons can be excited by ordinary light as conservation of
momentum is not required. Along with dipole plasmon resonance, multipolar resonance
also exists for small clusters or individual nanoparticles. The surface charge distribution
on nanoparticles alone distinguishes a dipole plasmon resonance from multipole
resonance. Thus surface of the nanoparticle plays a crucial role for the surface plasmon
resonance as it can alter the boundary condition for the polarizability of the metal. The
electrons in the nanoparticle cluster behave as an oscillator system, while the electrons in
bulk materials conduct themselves as a relaxator system.
Since the past few decades, scientists have tried to tap the rare size dependent
opto-electronic properties of metal nanoparticles through simulation, fabrication and
characterization [79]–[84]. When conduction electrons are confined and quantized in a
small volume it enhances the opto-electronic properties in nanocrystals [85], [86]. When
the wavelength of incident light is larger than nanoparticles, energy will be confined in
the small spatial regions through local excitation of SPRs. The field enhancement in the
14
spatial regions where energy is confined are used in a wide range of applications as
sensors in chemical and biological sciences [87]–[91] and Surface Enhanced Raman
Scattering (SERS) [71], [92]–[95], nano-optical devices [96], [97] energy storage [98],
[99] and near-field scanning optical microscopy [100]–[102]. Further, interesting field
enhancement arises when one resonant particle are brought close to another resonant
particle. Thus, when the resonant particles are vicinal to each other, the energy of the
particles are found at the interface between the particles. Additionally, the resonant
energy can transfer between the particles in vicinity leading to transport of
electromagnetic energy at length scales smaller than the diffraction limit. Further particleparticle interaction also control the linear and nonlinear optical properties of
nanomaterials embedded in matrices or as assembled into thin films. Thus, nanomaterials
as aggregates or in the form thin films provides opportunities to exploit unique properties
of these materials in electronic and optical device applications. The Mie’s theory
developed to solve Maxwell’s equations for individual spherical nanoparticles does not
hold good for aggregates of nanoparticles or for the field enhancement occurring at the
interface of the particles. For such scenarios, effective medium theory proposed by
Maxwell Garnett can account for optical absorbance behavior of metal nanoparticles
aggregated as matrices and thin films.
2.2 Mie Theory
The variation of colors of colloidal gold nanoparticles with size is an intriguing
scientific phenomenon in the early last century. Gustav Mie had applied Maxwell’s
15
equations with suitable boundary conditions in spherical coordinates using multipole
expansions of incident light’s electric and magnetic fields to explain the color of colloidal
gold solutions. The colloidal solution he investigated had spherical nanoparticles,
however his theory can offer exact solutions for ten other geometries such as cylinder,
parallelepiped, spherical shells etc. to name a few [61], [73], [75], [103]–[107].
2.3 Postulates of Mie Theory:
The Maxwell’s equations of geometries mentioned above can be solved using
Mie’s theory with the following assumptions. 1) The bulk optical and dielectric functions
of particle under investigation and its surrounding medium are extendable to
nanoparticles [108], [109]. 2) The boundary conditions of nanoparticles are explained by
electron density which has sharp discontinuity at the surface of the particle at radius R. 3)
the optical materials function of nanoparticle and its medium are input parameters. 4) The
wavelength of light interacting with metal nanoparticle should be at least twice larger
than its radius. Under these assumptions, the electric component of light is constant and
the interaction of light with nanoparticle will be governed by electrostatics instead of
electrodynamics. Under these conditions, quasi-static approximation takes effect.
2.4 Deviation from Sphericity:
Surface plasmon oscillations of metallic nanoparticles takes a twist when they
deviate from spherical to non-spherical shape [110]–[117]. When metallic nanoparticles
depart from sphericity, the longitudinal resonance and transverse resonance emerging
from such particles will no longer considered equivalent [110]–[112], [118]. The
16
longitudinal plasmon resonance will be long and red-shifted, and another peak for
transverse plasmon resonance [110]. To account for this phenomenon Gans offered a
modification to Mie theory.
2.5 Limitations of Mie Theory:
Mie theory was able to calculate the optical response of isolated single metal
nanoparticles only by following electrodynamics. It cannot account for variation in
optical properties emerging from polydispersity. Further, this theory works well under the
assumption that there is no interaction between the metal nanoparticles, however, in
reality new optical properties emerging from interactions between nanoparticles cannot
be ignored. Another significant drawback for this theory arise from the assumption that
dielectric constant of small metal nanoparticles is same as bulk, but opposite is true [119],
[120].
2.6 Effective Medium Theory:
It is understood that Mie’s theory does not hold well when metal nanoparticle
solution is concentrated as metal-metal interaction interferes with optical properties of
single metal nanoparticle. When a metal nanoparticle cluster is in close proximity to
another cluster and if the cluster - cluster to distance is smaller than five times the radius
of metal nanoparticle while lead to intricate extinction spectra due to single metal
nanoparticle and particle – particle interactions [10], [121]–[124]. Maxwell Garnett was
able to account for this observation through his effective medium theory [125]–[128].
This theory was able to account for the optical properties of metal nanoparticles that
17
exists as small close-packed assembly.
Effective medium theory works as long as
quasistatic limit is met for various shapes of particles. For small particles, optical
properties are due to property of the metal as well as property of the ensemble. This
condition is typically met in thin samples where the optical behavior of cluster containing
N particles will be Nth fold of the individual. However, if ensemble is comprises large
number of particles, N particle and Nth fold logic would not be observed. Under those
circumstances, inter-particle interactions outweigh the optical properties of the cluster
and isolated particle approximation does not hold good to explain the observed surface
plasmon oscillation [129]. Unlike the isolated metal nanoparticles whose optical
properties or surface plasmon oscillation depends on dimensions of the particle,
geometrical shape etc., the aggregated cluster particles optical properties are defined by
correlation length of spatial ordering, filling factors and structure of geometric ordering
to name a few. Such information regarding aggregates can be obtained via a statistical
average over a large number of aggregates and average volume fraction. These values
typically depend on synthesis conditions of metal nanoparticle, which aggregate to form
clusters. Most importantly, this theory can be generalized to several shapes of particles;
however, it is valid under quasi-static approximation conditions only. Being said that, the
assumptions of this theory are as follows: 1) the particle shapes are approximated to
spheres and aggregate shapes should be easily treatable geometries 2) particle sizes are
small such that scattering is negligible 3) the metal nanoparticles response to
electromagnetic field is assumed to be linear 4) chemical structural constituents may be
18
reduced to minima and it has only negligible proximity effects of sample surface are
present.
Based on the above assumptions, let us discuss now the quasistatic response of
spherical metal nanoparticles to electric field. For a polarizable particle, the dielectric
function is due to total of all contributions arising from electrical polarization that
includes neighboring particles. For the particle under investigation, the surroundings are
treated as homogenous on scale length that is larger than spatial correlations length,
however, for the vicinal particles contribution to the local field through scattering and
spatial arrangements are very significant and should be considered in detail. The
dielectric properties of such nanoparticles can be effectively represented using Lorentz
local field as:
………………. (2)
E0 is external field; Es is electric field arising due to polarization charges around the
sphere, Ed is electric field due to charges on the external surface of the nanoparticle, Enear
is the field arising due to dipoles inside the sphere. The above equation (2) can be
represented in alternative form as
……. (3)
where Emaxwell is defined as sum of external field and field from polarization charges on
the surface of Lorentz sphere. Another important assumption is the dielectric function of
19
material ɛm is real and effect of impact of the contiguity or proximity of sample surface is
negligible. Additionally, the Lorentz local field is assumed to act on particle as whole.
When colloidal nanoparticles are touching each other, a new embedding method
is employed to solve the Maxwell’s equations to understand how plasmons are affected
by the crystal field. The Maxwell Garnett approximation holds good for the interacting
metal nano spheres when filling fractions (f < 10-3) are low. However, when the filling
fractions are more than 10-3 collective properties become significant and Enear reduces to
0 as the scattering fields of the particles nullified via interference at the center of the
sphere. However, the electric field surrounding the sphere due to polarization of charges
Es should be considered and given by the equation (4).
…………. (4)
Similarly, the relationship between average electric field E and polarization P for local
electric field Elocal is defined by equation (5)
Elocal = E + 4πP/3………… (5)
The dipole moment, µ, and polarization of the nanoparticle are calculated using the local
field. Thus dipole moment is defined as
…………. (6)
20
Likewise, the P, the polarization is expressed as follows:
………. (7)
in equation (7) αi is polarizability of the ith particle and Ni is number density. Substituting
eqn (5) in eqn (7) we represent P as
…… (8)
The susceptibility (χ) and polarizability of nanoparticle with radius (r) and permittivity
(ɛ) are defined by eqn (9) and eqn (10) respectively.
……… (9)
…………………. (10)
When a nanoparticle satisfies quasistatic approximation conditions, then the
system will be substituted by effective medium, which behaves approximately like a
homogeneous material are described by, effective dielectric function,
composite samples. The effective dielectric function
ɛeff,
ɛeff
, of the
offers the linear response of
sample to external field in terms of polarizable properties of the particles. This effective
dielectric function remains constant even upon substitution of non-homogeneous sample
21
by its analogous effective medium like an intensive property. Thus
ɛeff,
can be
represented through Clausisu –Mossotti relation:
…….. (11)
When volume fraction “f” was introduced in eqn 10, it takes the form as shown in
eqn (12) which a familiar version of Lorentz-Lorenz equation:
……….(12)
If the particle under analysis is atom, then eqn (11) will be known as ClausiusMossotti equation. However, if it is a cluster of nanoparticles then eqn (11) can
represented as shown in equation (13), which is known as Maxwell Garnett equation:
….. (13)
Where Ʌ is
….. (14)
For isolated nanoparticle, the surface plasmon absorption spectrum is given by absorption
constant γa(ω),
22
….. (15)
Where,
The above Maxwell Garnett equation holds good under low filling factors f, and is
only applied for dilute ensembles of nanoparticles that interacts via far-field and it breaks
down when the nanoparticles are close enough for near-field to interact.
It is well seen now for dilute ensemble of nanoparticle aggregates, Maxwell
Garnett effective medium theory is capable of explaining the optical properties by
employing effective medium approximations. In the effective medium approximations,
the nanoparticle cluster or aggregate was substituted by effective object whose dielectric
constant is uniform. Reasonably accepted results for the optical spectra of clusters are
possible when the density of ensemble is suitably low and per particle polarization is
within the quasistatic approximation limits. However, when quasistatic approximation
conditions were not met by aggregate, the optical properties of such spherical ensembles
are explained by coupled multipoles [130]. The coupled multipoles method is able to
analyze aggregates composed of few hundred particles unlike the effective medium
theory which is around ten particles. For the coupled multipoles method, best results are
found when the particle size is small. For sufficiently small particles, the cluster may
23
have up to 100000 particles, and lattice of the aggregate can be defined using Fourier
transformations to find the sum of dipoles.
The optical response for aggregate of metal nanospheres to the incident light and
the scattered fields from other particles are from self-consistent solution, unlike for
macroscopic molecules optical response are governed by Maxwell’s equations for electric
and magnetic field. If nanoparticles size is less than the wavelength of the incident light,
the optical response hugely depends on dipole component of electric field, provided, the
higher order multipole components are not very large. The polarizability αi of isotropic
nanospheres are determined by the equation below:
……… (16)
Where r is the radius of sphere, and k=mo(2π/λ) is the magnitude of wave vector
for the dielectric medium; mo and a1 is real refractive index and function of size
parameter respectively.
As mentioned earlier, the optical response to aggregate of non-magnetic spherical
nanoparticles could be evaluated by self-consistent solution of electric dipole
polarizations, Pi, of every sphere in the superposed field of incident electromagnetic
radiation and dipole fields of other particles. Hence, the nanospheres aggregates can be
expressed as one dipole for every particle instead of several. Hence for given dipole in a
position ri,
24
……..(17)
In the above equation, Eloc(ri) is a sum of incident plane wave and retarded fields
as per the equation below:
……….(18)
Use of retarded fields, avoids the necessity of using explicit modeling of time
dependence of fields and polarizations. Hence,
…………..(19)
Above expression provides solution for the optical response of nanospheres
packed at a distance close enough to be called as aggregates.
2.7 Discrete Dipole Approximation Method (DDA):
For aggregates of metal nanoparticles the description is challenging and
complicated when compared with single particles.
Aggregates that has only few
particles, solutions to Maxwell’s equations can be achieved using Fourier transformation
methods to perform dipole sums. These calculations are often identical to discrete dipole
25
approximations (DDA) where each particle represents a dipole. All dipoles in the
aggregate are coupled together to attain the overall polarization response of the aggregate
[130]. Thus DDA facilitates to describe the arbitrary shapes, composition and sizes of
aggregates which are touching or coalescing [131]–[133]. This approach divides the
nanoparticle aggregate into several small polarizable cubes. Such induced dipole
polarizations are used to determine extinction cross-section of the aggregate. This method
was first proposed by Pennypacker and Purcell [134] and remained dormant until the
theory has found applications in chemistry by Van Duyne and Schaatz [135]. Now this is
one of the important computational tool to investigate the optical properties of
nanomaterials. The prime challenge while using this method is, too many elements are
necessary to describe a small aggregate that contains around 10 particles.
Significant developments were made in DDA theory to describe nanoparticles
which are not spherical using finite element discrete dipole approximation theory. This
approach divide the particle into many polarizable cubes. The dipoles induced in these
polarizable cubes are evaluated self-consistently, followed by extinction cross-section
were determined using the induced polarizations. Huge advantage of this method is it
evades the imposition of boundary conditions to the particles under investigation through
dividing the particle into elements and thus it allows the elements to interact via dipoledipole interactions only. Thus, a nanoparticle cluster under investigation is defined by a
cubic array of several N point dipoles that has polarizabilities represented as αi, centered
26
at position ri and the interaction of dipole with local electric field (Eloc) will induce
polarization are defined by equation (20).
……..(20)
However, for isolated particles, Eloc is defined by equation (21)
(21)
The incident wav amplitude and wave vector are denoted as E0 and k respectively. The
interaction matrix A takes the form equation (22)
.. (22)
k in equations (21) and (22) are defined as ω/c. When equations (21) and (22) are
substituted in equation (20), equation (23) will be arrived.
A'.P = E……. (23)
A' is the matrix derived from A in (21). Thus for equation containing a total of N dipoles,
E and P have 3N dimensional vectors and A' is defined as 3N × 3N matrix. Solving
equation (23) enables solution for P. Substitution of P in equation (24) leads to
calculation of extinction cross-section Cext
27
….. (24)
The above obtained solution will be exact for particles with finite size, however, for
particles with irregular shape the results are off with 5% of the exact extinction crosssection when optical response of bulk dipole lattice to bulk material when calculations
were converged with respect to dipole density. The downside of this approach is too
many elements are required to describe even a small aggregate.
2.8 Finite Difference Time-Domain Method (FDTD):
FDTD is computational electrodynamics modeling technique to obtain the optical
responses to nanoparticle aggregates of arbitrary shapes. This is arguably the simplest in
terms of implementation and concept wise. This methods uses grid based differential time
domain numerical modeling methods. It is capable of running simulation over a wide
frequency range in a single run. If particle under investigation is smaller than the
wavelength of light, efficient solutions are obtained through quasi-static approximations
and ray based methods are used to solve the particles for which wavelengths are shorter
than the particle under investigation.
The fundamental FDTD grid was first proposed by Kane Yee in 1966 [136] and
the acronym was tossed by Allen Taflove in 1980 [137]. The key points in of this
algorithm are as follows: a) all derivatives in Ampere and Faraday’s laws are replaced by
finite difference. Space and time are discretized such that electric and magnetic fields are
distributed over both space and time. B) Evaluate electric fields and magnetic fields one28
step at a time which is also defined as leapfrog manner. FDTD is widely used
computationally to address all problems related to electromagnetic wave interactions with
material structures. The applications of FDTD simulations range from predicting the
performance of photonic crystals, nanoplasmonics and biophotonics to name a few.
The FDTD technique divides time and space into discrete segments. Box-shaped
cells are used to segment space. However, wavelength is larger than these spaces.
Magnetic fields are located on the faces of the boxes while the electric fields are located
on the edges. This is called the Yee cell field orientation which forms the foundation of
the finite-difference time-domain technique [138].
This orientations quantizes time into steps that denote the amount of time a field
requires to move from one cell to another. There is an offset of the field values with
respect to change in time as a result of the offset in the space between the magnetic fields
and the electric fields. A leap frog schematic updates the magnetic and electric fields with
the magnetic fields computed after the computation of the electric fields relative to the
change in time.
The FDTD mesh (or grid) is generated from the accumulation of numerous FDTD
cells that together form a 3D (three-dimensional) volume [139] as shown in Figure 2.
Each FDTD cell is characterized by three electric fields starting at a common node that is
associated with the cells. This is the result of the overlapping of the edges and faces of
the FDTD cells that are adjacent to each other. The common node of the electric fields is
the origin of the three magnetic fields that characterize the faces of cell adjacent to the
29
node. Manipulation of the equations that compute the fields at specific locations allows
the addition of materials such as dielectrics and conductors within the FDTD generated
mesh. A salient example is setting the electric field computing equation to zero when
adding an efficiently conducting wire segment to a given cell.
Figure 2.4: Three magnetic fields originating from the common node [139].
This is because efficiently conducting substance or wire has an electric field that
is identically zero. A wire is formed by connecting the edges of numerous end-to-end
cells that are defined as efficient conducting materials.
This model allows for the addition of other different materials by applying similar
manipulations to the electric and magnetic field calculations, relative to the
characteristics of the materials elected.
30
Figure 2.5: The geometry of the spherical dielectric target.
The FDTD grid allows for the generation of a geometrical structure that results
from the association of numerous cell edges with the respective materials, with every box
representing a single FDTD cell [140]. The value a waveform is added at each step time
to the corresponding field value. The introduced waveform will be efficiently propagated
throughout the FDTD grid relative to the characteristics of each individual cell.
The FDTD simulation has one important constraint, the dimensions (size) of the
small box. This is because the box represents the upper frequency limit for the calculation
that has been employed, as well as the time step size. This technique employs a rule of
thumb that determines the minimum resolution at ten cells per wavelength. This also
serves as the upper frequency limit. While this is in theory, the cell size tends to
characterize a much smaller resolution which is important in resolving the features and
dimension of the simulated structure. These include the length or thickness of a wire.
31
2.8.1 One-Dimensional Simulation
The one-dimensional simulation using the FDTD technique is applied to the
simplest problems such as the simulation of a pulse propagating in a single-dimensional
free space. This technique employs the Maxwell curl equations in free space that are
time-dependent [141]. While the initial vectors of the equation (
and
) are three
dimensional, the one dimensional approach is applied by orienting the equations of the
magnetic field of the plane wave in the
direction and the electric field in the
direction.
This results in the approximation of the central differences for the spatial and temporal
derivatives as;
………..…….…..(25)
…………….…..(26)
The subscript
assumption that
and
denote time as
are incorporated in both time and space. The
to be found between the values of the
values before or after
. Both equations are founded on the
field. The
field is assumed
superscript indicates between which
it occurs. In the FDTD technique, time is implicit making
calculations easier and more accurate.
32
This results in the rearranged iterative algorithm;
………. (27)
… (28)
The calculations highlighted above are interleaved for both space and time. This
is evident in the fact that the new value of
of
takes into account the most current values
as well as the previous value of
. The one-dimensional simulation employs
absorbing boundary conditions in order to mitigate the reflection of
and
fields back
into the problem space [139]. This technique can also be employed in the simulation of
propagation in a dielectric medium. This is achieved through the addition of the relative
dielectric constant, represented by
, into the Maxwell equations.
2.8.2 Two-Dimensional Simulations
2D simulations are usually conducted on either the transverse magnetic (TM)
mode or the transverse electric (TE) mode. The TM Mode is comprised of
fields. The TE Mode is made up of the
,
,
,
fields. Two dimensional simulation
also takes into account the interleaving of fields in the calculations.
33
,
Two-dimensional simulations employ the perfectly matched layer (PML) as its
absorbing boundary condition (ABC). This technique is an effective way of accounting
for and distinguishing the unpredictable reflections that may be generated and go back
into the problem area. PML essentially states that a wave propagating in medium A
impinges upon medium b, the intrinsic impedances of the two media determines the
amount of reflection experienced. PML is also considerably flexible, and is represented
by equation 29;
…………(29)
But also taking into consideration that the permeabilities
and dielectric
constants of the two media determine the above formula;
……..……. (30)
The two dimensional simulation has to take into account the two conditions that are
required to form a PML. They include:
A- There’s constant impedance that moves from the background medium to the
PML. Where the impedance will be 1 with normalized units.
….. (31)
34
B- The relative permeability and relative dielectric constant in the direction
perpendicular to the boundary has to be inverse to those in the other directions.
This is represented by;
…….... (32)
……. (33)
The two-dimensional simulation has the ability to simulate a plane wave. This
wave can be simulated while interacting with an object by specifying the object in terms
of its electromagnetic properties, the dielectric constant involved in the problem and the
conductivity. The FDTD two-dimensional simulation also has the ability to simulate a
smooth transition from one medium to another. This is achieved by dividing all FDTD
cell into sub cells.
2.8.3 Three-Dimensional Simulation
This type of simulation is similar to two-dimensional simulation with the only
difference being the logistical problems that increase the complexity of the problem. This
is because this simulation employs all vector fields, with each field in three dimensions.
The simulation starts with Maxwell equations and assumes the notations as the
general assumption of normalized values is applied [139]. This will result in the
production of six scalar equations represented by;
35
…………. (34)
…………. (35)
…………. (36)
…………. (37)
…………. (38)
…………. (39)
The relationship between
and
is the same in one-dimensional, two-
dimensional and three-dimensional analysis with the difference being the presence of
three equations. Three-dimensional analysis also employs the use of PML with the only
difference being the introduction of three direction as opposed to two in the twodimensional analysis. One of the key constraints of the FDTD three-dimensional analysis
is the steps size for both space and time. These two elements influence accuracy, stability
of the FDTD technique and the numerical dispersion.
36
2.9 FDTD Simulation Software:
Problems that requires solutions through FDTD analysis are typically solved by
simulation software. FDTD analysis is required for applications stretching from
biophotonics to design of antennas to name a few. This technique is relatively new in
comparison to other analytical techniques such as method of moments, finite element
method and frequency domain techniques. FDTD commercial software packages made
entry as powerful research tool for simulations after satisfactory solutions for absorbing
boundary was addressed. Several research institutions and companies offer software
packages for FDTD simulations ranging from free to limited usage. Personal computers
had seen a huge transformation with reference to speed, bits and random access memory
since the beginning of this century and those developments made simulations by FDTD
software packages seamless in terms of computation speed, accuracy of analysis and
magnitude of problem that could be solved. Typically the bits of the computer accounts
for error in analysis arise from truncation of nanoprism. Higher the bits, lesser the error.
Processor speed accounts for time of analysis. The magnitude of electrical component
size from electromagnetic radiation depends on random access memory. Thus, higher the
random access memory of the computer, larger the variables that can be dealt by
computer. Additionally, grid cell dimensions can be made smaller and smaller with
increase in random access memory. While the developments in personal computation
had made the FDTD analysis simpler, dedicated hardware also developed for this purpose
to make the FDTD analysis further simple. However, the dedicated hardware are not
37
cost-effective hence it is not widely used. To alleviate the cost issues associated with
hardware, graphic cards meant for FDTD computation was also developed and widely
used.
Below is brief discussion about the types of software packages available for
FDTD:
EZ-FDTD: It is supported in Win9x, WindowsNT, Windows2000, and
WindowsME & Windows XP. Users will be able to create the models as they desire. It
uses same graphical interface to create models and display results. This software is
capable of generating error messages for invalid or illogical FDTD problems. If offers
movies and far-field points for electrical and magnetic fields. The latest version is
capable of solving problems with applications in antenna design, SAR studies, material
modeling, power plane decoupling analysis and many more. It offers a 30 day trial
version. The functionalities and features include Linux, and Windows platforms, voltage
and current probes, boundary conditions for PML, Mur or Liao etc.
Fidelity FDTD-Based EM simulator software: This is a full 3D-electromagnetic
simulator for modeling antennas, microwave circuits, waveguides etc., It can be used
online as well as downloaded to personal computer. MS Windows based menu-driven
graphic interface for construction of interactive 3D and planar structures. Radiating
boundary conditions modeled as various absorbing boundary conditions including PML.
Antenna structures can be modeled efficiently and accurately. Pre-defined coaxial port,
microstrip port, rectangular waveguide port, circular waveguide port and user-defined
38
port allow hassle-free port definition are available. It can have both far and near field
view. Integrated pre-processing and post processing are available. It is space and
simulation time efficient.
In a similar note, other software packages available for FDTD simulations are
Empire FDTD software package, Concerto FDTD software package, Optiwave FDTD
software package, XFDTD software package, Agnora FDTD software package, MEEP
FDTD software package etc. MEEP FDTD software is a free simulation software. All the
softwares for FDTD simulations discussed here had more or less similar capabilities. In
our research we have used Opti-FDTD software package to simulate the triangular
nanoprisms we conducted.
2.10 Lorentz-Drude Model (FDTD)
The Lorentz-Drude Model is an essential tool that depicts dispersion materials
that have their frequency dependent on the permittivity of the dielectric defined by the
sum of multiple resonance Lorentzian functions depicted below;
……… (40)
Where;
are the resonant frequencies
is related to the oscillator strengths
is the damping coefficient
39
is the permittivity at the infinite frequency
is the permittivity at
While the model exists and functions within the frequency model, FDTD is based
in the time domain, and as such is a time domain technique. This difference makes it
particularly suitable for simulating broadband. In order for FDTD to handle the fullwave-analysis the Lorentz-model has to be transformed to the time domain [138]. The
Maxwell’s equation contains the polarization philosophy which is used to complete this
transformation. Within the time domain, the Lorentz-Drude Model is depicted in the
following manner:
……………………………..………… (41)
…………….. (42)
……….. (43)
When implementing the first equation into the FDTD formalism, we employ rage
dielectric susceptibility function. This takes into consideration the polarization equation
approach. The dielectric susceptibility function is highlighted below:
………………………... (44)
40
OptiFDTD marks Drude material using the following equation;
……………………….…… (45)
Where;
represents the permittivity for infinity frequency
represents the plasma frequency
represents the collision frequency [138]
In conclusion, while FDTD technique is a useful tool, there is need to increase the
computation speed of the current FDTD. This procedure would programing-intensive and
may include optimizing computation loops for cache, using multiple CPU of a computer
in a parallel configuration.
2.11 Anisotropic Colloidal Assemblies
The huge attention gained by nanomaterials in the field of science and technology
arise from dimensions of the particles. At nanoscale, due to the size, shape-dependence,
surface to volume ratio, the physical, optical and electronic properties of these materials
make them an indispensable components in the contemporary materials chemistry [117],
[142]–[144]. Such nanoparticles are broadly classified into two types: isotropic and
anisotropic. For nanomaterials with isotropic shapes have material properties same
regardless of the directions. However, for anisotropic nanoparticles the physical,
mechanical and optical properties differ with directions. In the recent years, significant
accomplishments were made in controlling the sizes [145] of isotropic materials and
41
modification of surfaces of those particles [146]–[148]. Interest in synthesis of tailorable
anisotropic materials such as multipods [149]–[153], nanoshells [154]–[158], disks
[159]–[161], triangular nanoprisms [160], [162]–[164], rods [165]–[169], and cubes
[170], [171] is gaining attention for its interesting properties. The research in this field is
sheer driven by its inherent shape-dependent properties [172], [173]. for cutting-edge
technological applications such as sensors, photovoltaics, surface enhanced Raman
spectroscopy [174]–[177]. Some studies are promising to date to tailor these anisotropic
particles towards its final structure. Additionally these anisotropic nanoparticles may
serve as templates for generation of new nanostructure different from the template [178],
[179]. Of the several anisotropic structures reported so far in the literature is largely in
the field of nanorods. Nanorods made of combination of elements such as CdSe, CdTe
and titania, or as pure metals such as Ag, and Au and few more were reported [180],
[181]. Typically surface plasmon bands of nanorods exhibited a red-shift along long-axis
and small blue-shift along short-axis. Further, it was demonstrated that surface plasmon
resonance along long-axis is primarily affected by the aspect ratio of the rods. The
promising results from nanorods has triggered research in several anisotropic material
due its interesting optical properties.
Among the several shapes of anisotropic nanomaterials investigated for surface
plasmon resonance (SPR) applications, triangular nanoprism have been the center of
attraction owing in recent days. Triangular nanoprisms facilitates concentration of
electromagnetic fields at the edges and corners due to lightning rod effect. An ideal
42
triangular nanoprism is defined as polygon that has three congruent edge lengths and a
defined thickness. The SPRs of triangular nanoprisms are tunable across the visible and
near IR region (NIR) via manipulation of nanoprism edge length, thickness and
morphology of the tip. For triangular nanoprisms, multiple modes (dipole, quadrupole
and octupole) of SPRs are possible unlike spherical nanoparticles. Typically dipole and
quadrupole resonance are separated by 100 to 400 nm hence it can be resolved very well
in triangular nanoprism. The dipole and quadrupole modes of resonance originates from
direction and degree of polarization of electron cloud relative to incident electric field of
the light. Dipole plasmon resonance arises when electron cloud surrounding the
nanoparticle moves either parallel or anti-parallel direction to the applied electric field.
For quadrupole mode of resonance, around half of the electron cloud surrounding
the nanoparticle moves parallel and other half moves anti-parallel. Higher order
resonances beyond dipole and quadrupole are observed for triangular nanoprism with
high aspect ratio through complex polarizations which will not be discussed here as it is
beyond the scope of this dissertation.
2.10.1 Effect of Snipping or Truncation
We have discussed the interesting optical properties of triangular nanoprisms
made up of noble metal nanoparticles. However, the triangular nanoprisms that are
synthesized in laboratory are not perfect triangular nanoprisms instead they are mixture
of particles which had different degrees of truncation along with ideal ones. When the
truncation of nanoprism is huge, they no longer are categorized as triangular nanoprism
43
instead they are referred as nanodisks or nanohexagons. Intense research are underway by
chemists to synthesize ideal triangular nanoprisms. Snipping or truncation that arises
during the synthesis of triangular nanoprisms also found to impart some interesting
plasmonic properties to the materials. It was observed by researchers that the snipping
introduces a red or blue shift to plasmonic resonance peaks. This will be discussed in
detail elsewhere in this dissertation.
2.11.2 Effect of dielectric on plasmonic properties
Apart from the structural parameters of triangular nanoprisms such as edge length,
thickness and truncation, dielectric environment of the nanoprism also affect the
plasmonic properties [182]–[184]. Qualitatively, plasmon wavelength and refractive
index of dielectric are directly proportional to each other [117]. Further the optical
properties of nanoparticles were found to be very sensitive to particle morphology. The
refractive index sensitivity for spherical nanoparticles were found to be 100 nm per
refractive index unit [185], however, for tetrahedral nanoparticles the sensitivity was
found to be 200 nm per refractive index unit [186]. The general trend reported in
literature was larger the aspect ratio of the nanoparticle, larger the sensitivity to dielectric
medium. In another report by Xue et al, silver nanoprisms coated on glass substrate
exhibited reversible color changes when they were wet and dry. The reversible color
changes observed for silver nanoprism arise from plasmonic sensitivity to surrounding
refractive indices [187].
44
Generally, plasmon resonance of metal nanoparticles are investigated in
transparent media whose dielectric function does not interfere with optical frequency of
interest. When refractive index or dielectric medium is changed, the plasmon resonance
frequency changes too. Thus plasmon resonance frequency is a measure of refractive
index of the surroundings of a metal nanoparticle. This phenomenon leads to molecular
detection of biological molecules. Biomolecules have refractive index different from
water, hence, when biomolecules bind to surface of plasmonic metal nanoparticle, shift in
plasmon resonance frequency occurs which enables the detection. Thus presence of
dielectric does not require fluorescent agents, radioactive or other labeling agents to
monitor or detect the binding of biomolecules. Gold nanoparticles are widely used for
this specific applications owing to its biocompatibility and readiness to its biofunctionalization ability with sulfur containing functional groups.
2.12 Synthesis of Nanomaterials:
Nanomaterials are conventionally synthesized by one of the following four methods
described below depending on the sources of the nanomaterials or the desired features of
the final product.
1) Inert gas condensation: in this process the precursors of the nanomaterials are
decomposed at elevated temperatures followed by condensation or precipitation
of nanoparticles. This method generates nanoparticles with contamination free
surface with ultrafine crystallite size
45
2) Physical or chemical vapor deposition: in this process, atoms or molecules are
deposited on appropriate substrate by vaporizing the precursors of the
nanomaterials. This method is also suitable for producing nanocomposites by
deposition of different precursors in simultaneous or consecutive fashion.
3) In the third method, nanomaterials are synthesized by creating imperfections
(dislocations, grain boundaries) in a perfect crystal via high energy irradiation,
ball milling or through shear to name a few.
4) Precipitation or crystallization: nanomaterials will be crystallized or precipitated
from unstable condensed phase from glasses or precipitation via supersaturated
solutions of liquids or solids.
The above four categories are the common ways to size nanomaterials, however
several variations of these processes were to produce nanocomposites with tailorable
compositions and features. Being said that, two broad and common synthetic techniques
are physical and chemical methods.
The common physical methods are inert-gas evaporation technique (Figure 2.6),
sputtering, mechanical deformation etc, however they suffer from poor control on
features of the nanoparticles being prepared and contamination. Physical methods are
useful to synthesize the nanomaterials in large scale. Chemical methods of synthesis
yields nanoparticles with high homogeneity via mixing at molecular level. On that
context, we are going to discuss current developments reported in the literature to
synthesize anisotropic nanoprisms of gold and silver.
46
Figure 2.6: Schematic representation of experimental set-up for preparation of
nanoparticles via inert-gas condensation method [188].
2.13 Synthesis of Triangular Nanoprisms:
Synthesis of triangular nanoprisms are broadly classified into two types: a)
Thermal b) Photochemical. The thermal synthesis further classified into two categories
based on the synthesis medium as aqueous phase and organic phase synthesis. Similarly,
photochemical methods are classified into visible light methods and UV and radiolysis
methods based on the wavelength of employed during the synthesis. We present here a
brief discussion of both methods (thermal and photochemical) in this literature review.
47
On that note, we first discuss, thermal methods of synthesis of gold and silver triangular
nanoprisms.
Figure 2.7: Synthesis of triangular gold nanoprisms along with some spherical
nanoparticles. Figure adopted from reference [189].
First report on synthesis of triangular gold nanoprisms (Figure 2.6) as part of
mixture of hexagons and pseudospherical particles when they reduced the chloroauric
acid using salicylic acid were published by Malikova et al [189]. The UV-Vis spectra of
the colloidal solution exhibited two SPR (surface plasmon resonance) peaks
corresponding to spherical particles in the visible region and longitudinal modes of
anisotropic particles in the near infra-red region. The SPR peak due to anisotropic
particles were very broad due to polydispersity in size and shape of the anisotropic
structures. Followed by this report, Zhang and coworkers [190] reported synthesis of
48
gold nanoparticles through reduction of chloroauric acid using sodium sulfide. Such
synthesized particles also exhibited SPR peak in the near IR region which was accounted
for anisotropic triangular nanoprism. Followed by this two initial reports, methods were
developed to produce gold nanoprisms with control in size and shape by tweaking the
experimental parameter. Ah et al [191], synthesized gold nanoplates using sodium
citrate as reducing agent for hydrogen tetra chloraurate in presence of poly vinyl
pyrrolidone(PVP). By tuning the molar ratios sodium citrate and PVP in reference to
HAuCl4 the geometric shape and size were tuned to the width between 80-500 nm and
thickness ranging from 10-40 nm (Figure 2.7). Importantly they were able to gain control
in dispersity of size and shape. The sodium citrate used in the synthesis generates small
number of gold nuclei as seeds towards the lateral growth of the nanoprism.
Figure 2.8: Scanning electron microscopy images of gold nanoprisms with various
dimensions synthesized using PVP to HAuCl4 ratio. Figure adopted from reference [191].
Mirkin and coworkers [192] also reported the synthesis of gold nanoparticles
using cetyl trimethyl ammonium bromide (CTAB) as capping agent through three-step
49
growth of gold nuclei seeds in aqueous media. Ascorbic acid was employed as reducing
agent. In that strategy, they were able to synthesize a mixture of spheres and triangular
nanoprisms exclusively with better control in size distribution in a homogeneous way.
Interestingly, the studies of optical properties of gold nanoprism exhibited optical
features characteristic to dipole and quadrupole plasmon resonance. This was the first
report published for observation of quadrupole plasmon resonance.
High yield synthesis of Ag triangular nanoprisms were reported by Chen et al
[193]. Their synthetic strategy has two important steps: 1) seed mediated growth in
presence of CTAB for preparation of truncated silver triangular nanoprism 2) aging of
colloidal silver nanoprism solution. Aging process was critical in determining the shape
of nanoparticles. TEM analysis of colloidal solution of silver before aging has revealed
particles with size below 10 nm were spotted, which authors claim as seeds for the
growth of larger particles through Ostwald ripening process. Such synthesized particles
had thickness around 28 nm and diameter approximately 60 nm. In another research
report published by Carroll and coworkers, had similar observations [160]. They
synthesized truncated triangular silver nanoprism using ascorbic acid as reducing agent
and CTAB as soft template. Synthesized particles had exhibited 4 absorption bands
between 35 nm and 552 nm which corresponds to in-plane and out-of-plane dipole and
quadrupole plasmon resonance. Growth of triangular silver nanoprisms were investigated
by changing the metal ion to reducing agent ratio, CTAB concentrations, pH, effect of
different reducing agents and seed concentrations [194].
50
Xia and coworkers reported the synthesis of silver triangular nanoprism by
reduction of silver nitrate via sodium borohydride reduction in presence of PVP and
sodium citrate. This synthetic approach produced silver nanoprisms with less rounding.
Additionally, this synthesis utilized thermal and photochemical approaches in aqueous
solution. Light was found to be important for formation seeds, while heat aids the growth
of seeds into larger structures. Thus far, we presented the reports on strategies to
synthesize triangular silver nanoprisms in shape selective fashion. Mirkin research group
reported synthesis of triangular nanoprism via thermal method with modest control over
edge length and thickness [195]. In this method, silver nitrate was reduced using
trisodium citrate in presence of PVP by changing the amounts of sodium borohydride.
Amount of sodium borohydride employed during the synthesis played important role in
regards to the conversion of silver nanoparticles to triangular nanoprisms as well as the
edge length. In addition, thickness of nanoprism affects the optical properties
significantly than the edge length. Presence of PVP prevents aggregation of anisotropic
nanoparticle, whereas citrate controls the face selective growth of triangular nanoprisms.
Biological organisms, environments and molecules were also investigated in the
thermal synthesis of gold and silver triangular nanoprisms to tune the structural features.
Pseudomonas stutzeri AG259 a bacterial strain known to accumulate silver ions were
employed in synthesis by Klaus et al [196]. The poles of bacterial cell had accumulated
silver ions in triangular and hexagonal shapes. The silver fabricated to anisoptropic
structures were in elemental form and each cell had approximately 5 or less
51
nanostructures. The resistance to silver by Pseudomonas stutzeri AG259 and formation
silver crystals were found to depend on physical and chemical growth parameters. pH,
incubation time, effect of light, culture composition was found to tune the size and
morphology of the particle. Synthesis of gold nanoprisms were reported using the
extracts of plant materials [197]–[199] such as seaweed, aloe vera and lemon grass. The
plant extracts serve as both reducing and capping for the synthesis of triangular
nanoprism. When aurochloric acid were reduced by lemon grass, seed nanoparticles form
first, followed by aggregation. The anisotropic structures arising from aggregation had its
aspect ratio increasing over the time. This method yields more than 45% of gold
nanoparticles in the form of triangular nanoprism. Further triangular nanoprism formed
were is a mixture of perfect and truncated triangular nanoprism. For synthesis of gold
nanoprisms aided by seaweed extract, yields were as high as 80 -90% and tuning of
lateral nanoparticles size were achieved to the extent of 200-800 nm. The conclusion
made by the authors regarding this synthesis were, neutral pH and ambient temperature
were the optimal reaction conditions for high yields of nanoplates. Further, initial reactant
concentrations were found to tune the particle edge length.
In addition to plant extracts, genetic materials such as proteins and nucleic acid
were also employed to synthesize triangular nanoprism. These genetic materials found to
control the growth of nanoparticle. Johnson and coworkers have reported the synthesis of
via enzyme mediated biomineralization process. Gold (III) chloride was incubated with
potassium hydroxide and sodium ascorbate under ambient conditions. Morphology
52
controlled synthesis of nanoprisms affected by two key factors of polypeptide: a) affinity
for gold 2) possessing catalytic function. The creation of low pH environment at the
vicinity of growing crystal and blockage of (111) crystal face is crucial for nanoprism
formation [200].
Ultrasound and microwaves are widely used in the synthesis of nanomaterials.
The cavitation produced by ultrasound creates shockwaves in synthesis solutions which
affects the surface of nanoparticles leading to distinct shapes and structures [201]–[203].
Meanwhile, microwaves heat the synthesis solutions very rapidly than conventional hot
plate leading to brief crystallization times and homogeneous nucleation [204]. Perfect and
truncated gold triangular nanoprisms were synthesized using polyol (ethylene glycol) by
microwave irradiation in a pulse or continuous wave fashion of solution containing PVP
and HAuCl4. Such synthesized nanoparticles exhibited three bands characteristic of platelike nanoparticles. Interestingly authors reported the square nanoprisms for the first time.
Formation of nanoplates were facilitated by high temperatures achieved by microwave
radiation using ethylene glycol [204].
Sonochemical methods are extensively used used for synthesis of nanomaterials.
Jiang et al reported the synthesis of nanoplates by reduction of silver nitrate with
dimethylformamide in presence of PVP [201]. Transmission electron microscopy and
UV-Vis studies led to following observations: a) reduction of AgNO3 yields prism-like
seeds with initial dimensions of 2-5 nm spherical particles b) seeds on rapid dissolution
and rapid growth form larger crystals c) larger crystals upon slow growth form
53
monodispersed silver nanoplates through Ostwald ripening. The ultrasound was found to
accelerate the ripening process as well as control the size of as-synthesized particles.
Presence of PVP induces the selective crystal growth of plate-like particles. In another
study by Cai et al, ultrasound synthesis of gold nanoprisms were reported via reduction of
HAuCl4 using ethylene glycol in presence of PVP [205]. Ethylene glycol serves the role
of solvent as well as reducing agent. Experimental analysis indicates PVP and ethylene
glycol concentrations were crucial for formation of nanoprisms. For HAuCl4
concentration of 0.5 mM, varying the concentrations of PVP from 100 -200 mM favors
formation of nanoprism. When PVP concentration exceeds 200 mM, irregular
morphologies were formed. Additionally, it was observed that aging time is crucial for
manipulation of morphology. Sample synthesized through irradiation of ultrasound for
120 min that was aged for one week had nanoprism size of 70-90 nm which exhibited inplane and out of plane dipole plasmon resonance peaks. Aging beyond one week induced
for further growth in nanoprism. To the aged solution, fresh addition of HAuCl4 found to
increase the size of gold nanoprism which was confirmed by corresponding shift in
optical properties of nanoprisms.
In comparison to synthesis strategies being explored for nanoprism synthesis in
aqueous media, organic mediated synthesis is far from few as it requires elevated reaction
conditions. Liz-Marzan et al have reported the synthesis of silver and gold nanoprism in
DMF [206]. Silver nanoprisms were synthesized by reduction of silver perchlorate.
Under reflux condition, the nanoparticles synthesized for found to be have homogeneous
54
size distribution. Heating via microwave irradiation also explored by them, which
supports formation of homogeneously sized nanoparticles. Synthesis in the absence of
PVP leads to aggregation of nanoparticles. For microwave induced reduction, average
size of nanoparticles synthesized were independent of concentration of PVP. Molecular
weight of PVP used during the synthesis found to affect the features of nanoparticles
synthesized. High molecular weight PVP yields nanoparticles who bands are sharper,
symmetrical which can be correlated to uniform size distribution. Lower molecular
weight PVP yields larger particle size. Further, synthesized nanoparticles exhibited more
stability in ethanol than water which was attributed loss of stability of PVP due to high
polar nature of water. Sarkar et al also investigated the synthesis of silver nanoprisms,
using formamide [207]. When polyethylene glycol (PEG) was used along with
formamide, array of triangular nanoprisms were found. However, when PVP is used
along with polyethylene glycol, at a ratio of 1:1, nanospheres were also formed along
with nanoprisms. The ratio of PVP to PEG provided the opportunity to tune the ratio of
nanospheres to nanoprisms.
So far we have presented the brief literature reports regarding the thermal
synthesis of silver and gold triangular nanoprisms. Now we present a discussion of
progress made in light mediated synthesis of nanoprisms. First report on synthesis of
silver nanoprisms were reported by Mirkin research group [142]. It is a photo induced
method for conversion of large amounts of spherical silver spheres to triangular
nanoprisms. The synthesis procedure involves reduction of silver nitrate with sodium
55
borohydride in presence of trisodium citrate. Bis(p-sulfonatophenyl)phenylphosphine
dihydrate dipotassium salt solution (BSPP) was added dropwise which acts as stabilizing
agent and the reaction mixture was exposed to white light. A series of color changes were
observed over 70 hours ranging from yellow, green and blue. During that time when
reaction mixture was monitored by UV-Vis three new bands were appeared while the
peak due to nanosphere was vanishing indicating the spheres were converted to
nanoprisms. Synthesis can be turned on or off via tweaking the exposure of light with
appropriate wavelength or presence and absence of citrate ions and rate of reaction was
affected by citrate to BSPP ratio [179]. Formation of nanoprism had induction, growth
and termination stages. Growth of nanoprisms were achieved through Ostwald ripening
process using smaller Ag crystals as seeds and the reaction was terminated when all small
particles were consumed. Formation of triangular nanoprism was subject of intense
debate. Two theories were put forward were formation of nanoprisms are a) light driven
ripening process through transition from silver nanospheres [208], [209] b) oxidation and
re-deposition [210]–[212]. When Brus and coworkers synthesized silver triangular
nanoprisms in the absence of BSPP, it had a wide size distribution of prisms formed and
nanoprism conversion was incomplete. The kinetics studies indicated that nanoprisms
were formed by oxidative etching of Ag and subsequently a reduction process of silver
ions by citrate photooxidation. Further this studies ruled out the interference of photo
induced thermal heating and optical forces [213]–[215]. If spherical nanoparticles formed
initially are the ones being transformed to nanoprisms, approximately it would need
56
around 30 seeds to make a prism. For particles as many as 30 to come together, such a
process will have complex kinetic order. Reaction kinetics studies suggested autocatalytic
first order, thus fusion concept for formation of prisms were ruled out. Alternately,
oxygen in the seed solution dissolves silver to form silver ions, which is supported by the
fact that significant increase in pH of the growth solution. The primary role of silver seed
particles is to serves as source for silver ions which can be re-deposited on aging silver
nanoprisms. Additionally, the deposition and redeposition process are very crucial to size
of seed particles. Typically, larger the size of nanoparticle, higher its reduction potential.
Thus when silver particles go beyond a certain size, it will be tough to oxidize it, hence,
prism formation will be affected [216].
Sun and Xia, reported the synthesis of silver nanoprisms using PVP as stabilizing
agent and halogen lamp with UV cut-off filter [217]. They were able to achieve the
triangular nanoprism morphology regardless of whether PVP is used or not during the
synthesis. PVP found to affect the size distribution of silver nanoparticles being
synthesized. In addition to PVP, polyvinyl alcohol and sodium dodecyl sulfate were also
studied as stabilizing agent. They concluded that for successful synthesis of nanoprism,
the seed particles should be kept under 10 nm. Gehlen and coworkers reported the
synthesis of nanoprisms using two PVP of two different molecular weights i.e. 29000 and
58000 gmol-1 [217]. Molecular weights of PVP found to influence the stability of the
synthesized silver nanoprisms. Low molecular weight PVP was found to yield more
photostable nanoprisms than high molecular weight PVP. The other variable found to
57
affect the synthesis of nanoprisms are pH, use of nucleophiles and ligands [218].
Synthesis of nanoprisms via oxidative dissolution process were facilitated by use of
nucleophiles. Nucleophiles used during the synthesis would build up excess negative
charge in the interior of nanoparticles which aids the removal of electrons by oxidants
[142], [210], [211], [219], [220].
Xue et al reported the synthesis of silver nanoprisms using gold seed particles
[221]. The gold seed particles play a dual role in the synthesis as plasmonic cores as well
as experimental labels to evaluate the role of plasmonic excitation in conversion of
spherical silver nanoparticles to triangular nanoprisms. When a solution prepared with
Au/Ag particle with particle size of 11 and 5 nm respectively at a ratio of 1:10 was
irradiated with 550 nm light for 5 h, the outcome was silver nanoprism with Au core. The
nanoprism had an average edge length of 76 nm and 14 nm thickness. The thickness of
nanoprism was found to be dependent on diameter of the gold cores employed in
synthesis. The core-shell structure of silver nanoprism formation involves two steps: 1)
the dipole plasmon resonance of gold nanoparticles were excited by incident light 2)
deposition of silver layers induced by gold plasmon resonance. When the gold spheres
were replaced by gold triangular nanoprism as seeds, bimetallic core-shell structures were
not observed at irradiation wavelength of 550 nm. However when the irradiation
wavelength was changed to 1064 nm, silver nanoprism shell with gold prism core was
formed. Thus through this experiments, it is concluded that excitation wavelength also
plays a crucial role in formation of nanoprism.
58
So far we have presented the discussion on synthesis of triangular nanoprisms limited to
just white light. Chergui and coworkers first investigated the effect of irradiation
wavelength and shape of nanoparticles (Figure 2.8) [209]. First, spherical nanoparticles
were prepared via sodium borohydride reduction of silver nitrate and they split it into
multiples identical samples.
Figure 2.9: synthesis of triangular nanoplates after evaporation of solvent as seen in
TEM. Figure adopted from reference [209].
Those identical samples were initially exposed to light from fluorescent tube.
After an induction period, the nanoparticles color changed from yellow and green. At that
point, they employed various filters to control the irradiation wavelength from the same
source. Orange filter had predominantly produced triangular nanoprisms with very high
aspect ratio. For broadest blue filter, triangular nanoprisms of smaller size were the major
product, however when they used the narrowest blue filter, cubic and octahedral particles
were formed. Effect of irradiation wavelength on shape control were explained by
authors through photo-oxidation and light-induced coalescence and growth. During the
59
induction period photo-oxidation occurs, and growth occurs when filters were used.
Interestingly they were able to pause and resume the reaction by moving the reaction
solution to dark and light respectively [209].
Brus and coworkers synthesized silver nanoparticles photochemically from
adsorbed silver ions in the presence of citrate using laser [212]. If colloidal seed solution
has particles with different size and shape, larger particles in the seed solution grow
fastest. Citrate molecule employed in the synthesis play a crucial role as capping ligand
for Ag nanoparticles and to photoreducing agent. The three carboxylic acid molecules in
the citrate, two of them bind with silver and the third one involves in colloid stabilization
via electrostatic repulsion. Additionally citrate act as reducing agent too. The silver ions
concentration in the solution determines the ultimate size of the particles and the aspect
ratio is controlled via the irradiation wavelength. The aspect ratio of synthesized particles
are higher when size irradiation wavelength is high and vice versa.
Mirkin and coworkers have reported anisotropic synthesis of silver nanoparticles
by controlling the plasmonic excitation [219]. In that study they employed xenon lamp
coupled with band pass filter. The result was prisms with bimodal distributions in size
was produced. The edge lengths were found to be 70 nm and 150 nm but they had same
thickness around 10 nm. Bimodal distribution can be converted to monomodal
distribution when two different excitation wavelengths were used together. When
primary irradiation wavelength of 550 nm was used bimodal distribution was observed.
However, when secondary irradiation wavelength of 450 nm was used along with 550
60
nm, only unimodal size distribution size was formed. When secondary radiation
wavelength was kept constant and primary irradiation wavelength were changed from
450 nm to 750 nm results in linear increase of edge length. The bimodal and unimodal
particle size distributions were explained by particle fusion mechanism in an edge
selective manner or growth of nanoprisms reaching the maximum size controlled by
light.
In another report by Mirkin and coworkers, pH was used as a tool to synthesize
the silver nanoprisms (Figure 2.9) through single-beam excitation [222]. In the previous
synthesis discussion, a larger triangular nanoprism is being formed through coalescence
of 4 small nanoprisms [219]. In this synthesis they prevented accumulation of 4 triangular
nanoprisms coming together by controlling the pH which in turn executes inter-prism
repulsion.
Figure 2.10: pH controlled synthesis of silver triangular nanoprisms at irradiation
wavelength of 550 nm at pH 11.2. Figure adopted from reference [222].
61
When silver nanoparticles were irradiated with 550 nm light at an initial pH of
9.5. Bimodal particle size distribution was observed at pH of 7.4 through addition of
nitric acid. However, when sodium hydroxide was added to the seed solution to raise the
pH to 11.2, unimodal prisms were only observed. For such prisms the edge length
corresponds to smaller prism in the bimodal mixture observed at pH of 9.2. At pH value
above 12, the reaction does not yield any prisms as high hydroxide concentration
effectively removes the silver ions in the solution, without it, no reaction was observed.
Further at such elevated basic conditions a passive layer of silver hydroxide forms which
prevents the photoreaction.
Xu and Lombardi coworkers presented an alternate pathway to tune size
dispersity in triangular nanoprisms [223]. They employed monochromatic irradiation
source with different laser wavelengths for irradiation of seed solution. The synthesis
solution contains silver seeds, silver ions and citrate ions. They observed that both size
and shape were affected frequency and power of the incident light. The optical properties
exhibited by synthesized particles were found to be correlated to excitation wavelength.
The mild laser power contributed to bimodal distribution, however, stronger laser power
resulted in a monomodal distribution of particles. Lower laser power yielded particles
that are pyramidal and pentagonal in shape, while higher laser power yielded planar
triangular shape nanoparticles. The growth process of particles involves, inducing and
accumulation of nanoseeds to form intermediates followed by exciting the SPR of
62
intermediates that drives the directional growth into nanoparticles and finally truncation
and regrowth to form monodispersed silver nanoparticles.
In another interesting report by Liz-Marzan and coworkers, silver nanoprisms
were synthesized by reduction using sodium borohydride in presence of trisodium citrate
and PVP [208]. The reaction mixture was exposed to light emitting diodes (LED) with
different wavelengths at very low intensities. The silver nanoprism irradiated with light
of 653 nm, very high edge length of 242 nm. The higher temperature employed in the
reaction aid for faster completion of reaction without affecting the size or shape of final
particles. A quasilinear dependency of particle size was found with respect to irradiation
wavelength. The nanoprisms were formed at the expense of preformed silver seeds.
Zanchet and coworkers investigated the kinetics of formation of silver nanoprisms
synthesized using sodium borohydride reduction in presence of sodium citrate [224]. The
spherical seeds were exposed to visible light with wavelengths of 500, 550, 600 and 650
nm in presence of excess of silver nitrate and sodium citrate. When wavelength filters
were used, the silver deposition on seed particles was very slow until prism formation
was observed. This was due to the fact that seed particles plasmon excitation was far
from filter wavelength. Longer the wavelength used for irradiation, longer the time taken
for completion of the reaction and particles had longer edge lengths. The prism
morphology was seen even when little to no light was absorbed by seed particles. This
observation suggests plasmon excitation is not necessary for formation of prismatic
morphology. Paul et al reported the synthesis of silver nanoprisms on a solid substrate. In
63
that method, small nanotriangles, were embedded on the substrate followed by irradiating
in the seed solution. When linearly polarized laser was irradiated, the triangular
nanoprisms shown preference towards the direction with tip being parallel to polarization
direction.
There was not much precedence in the literature for the synthesis of silverdielectric-gold sandwich we proposed in this thesis. Spin coating will be an ideal starting
point to investigate the surface plasmonic properties of the sandwich structure
experimentally [225]. To tap the identified advantages through simulations of sandwich
structures, synthesis of those materials will pose a challenge for synthetic and material
chemists.
2.14 FDTD Simulation Parameters:
All FDTD simulations were performed using OptiFDTD simulation software. The
triangular nanoprisms of gold and silver investigated separately and as sandwich were
constructed using OptiFDTD software. The procedure for construction of triangular
nanoprisms of silver and gold were same as well as the sandwiches. The first E and B
nodes are taken to be zero since there are no source in the field prior to the start of the
simulation. The steps we carried out to do simulation is outlined here as follows:
Layout Creation Steps: Commercial software Opti-FDTD was used for
simulation of gold nanoparticles on 3D surface Plasmon. The procedure for simulation is
as follows:
64
Layout creation steps: from the start menu OptiFDTD waveguide layout designer were
opened, followed by in the programs section, optiwave software were chosen to open a
waveguide layout designer window. The initial properties dialog box appeared when new
project was created using OptiFDTD_Designer file menu.
Gold_Au_Lorentz_Drude_Model file was dragged from the material folder in
Master to
FDTD_dispersive folder under Materials in the current project.
Gold_Au_Lorentz_Drude_Model
was
stored
under
this
project.
In
the
OptiFDTD_Designer1, Channel folder can be found under the Profiles folder through a
right click. Choose New, followed by a Channel Profile dialog box pops up. In the
dialog box, profile name, layer name (layer 1), width (0.1), thickness (0.1), and offset
(0.0) were described. Gold_Au_Lorentz_Drude_Model was selected from the material
list and added to the channel profile followed by click store. After this, we went back to
initial properties dialog box and the following information were fed into the appropriate
box: width 0.1 μm, profile as ChannelPro1, wafer length – 0.6 μm (z-direction), and
width 0.3 μm (x-direction). Cladding material is air with thickness of 0.3 a(y-direction)
and air also serves as substrate material with thickness 0 (y-direction). OptiFDTD
Designer window appeared after click OK in Initial Properties dialog box.
A nanoparticle layout was drawn as triangular nanoprism and the shape of
waveguide and position was adjustable in the layout window by making double click on
the sphere. The position x, y, z of sphere waveguide were chosen as 0, 0.15 m, 0.35 m
respectively with a radius of 0.05 m. For further simulations, only the radius was changed
65
from 0.01 to 0.07 with an interval of 0.01 m without changing other parameters. At this
point, we can see the layout in the 3D mode under the 3D layout model tab.
Defining Input Wave: a Vertical Input Plane was chosen from the Draw menu
and the input plane properties were defined as Gaussian Modulated Continuous Wave,
with a wavelength of 0.55 μm followed by it was set to the time domain input waveform.
To the time domain input plane time offset and half width were chosen as 4.0e-15 and
0.8e-15 seconds respectively. The other general information for the Input Plane were
described as follows: input field traverse – rectangular, z position – 0.2 μm, plane
geometry – positive direction and finally it was labeled as InputPlane1. The center
position setting for X,Y are 0.0 and 0.15 μm respectively with halfwidth for X and Y as
0.2 μm. The effective index was chosen as Local and polarization as Linear Y with
amplitude of 1.0 (V/m2). With that we defined all the parameters for input plane.
Defining Simulation Parameters: simulation was performed through Simulate
3D Using 64-bit Simulator. The mesh size along X, Y, Z were chosen as 0.004 m. The
boundary conditions for X and Y direction were chosen as PBC and for Z direction as
APML. The values for PML boundary condition is, anisotropic PML layer number -16,
theoretical reflection coefficient – 10e -12, real anisotropic PML tensor parameter – 60.0,
power of grading polynomial – 3.5 and chosen to run 4000 time steps with sampling time
interval of 2.
Under the Spectrum tab, number of samples was set to 101, start
wavelength is 0.4 μm and end wavelength is set to 0.9 μm.
66
Observation Objects Setup: The observation point monitors the time domain
and frequency domain response. The observation area is used to calculate power
transmission ration and normalized power versus wavelength. The observation XY
plane placed next to sphere in the layout with center horizontal offset along z-directions
as 0.5 μm, center vertical offset along x-direction 0.0 μm, center depth y-direction as 0.15
μm, X and Y lengths as 0.3 μm and labeled as ObservationArea1 with data components
Ex, Ey, Hx, Hy. ObservationArea2 was set as above with center horizontal offset along
z-directions as 0.1 while maintaining all other parameters the same. Power spectral
transmission function was obtained from observation 1 and observation 2 will obtain the
power spectral reflection function.
Performing the 64Bit-FDTD Simulation: Now, we are ready to run the
simulation, as we have defined all required parameters for simulation.
When the
simulation is in progress the progress window represents the status of simulation,
Snapshot feature lets us to view the intermediate simulation results. After the simulation
is done, results can be viewed in analyzer.
67
Chapter 3
Study of the Snip Effect in Resonance of Gold and Silver Triangular
Nanoprisms
3.1 Introduction
The frequency of the LSPR however, depends on variables such as effective mass
and density of the free electrons, and strongly varies with the shape and the size of the
nanoparticles, as well as the wavelength-dependent permittivity of the nanoparticle and
its surrounding medium [226].
Plasmonic properties of gold and silver nanoparticles in particular, have found
several applications in recent years including in bio-sensing and chemical sensing [227],
[228] , and in SERS spectroscopy technique [229], [230]. Significant progress and
understanding has been made to explain the relationship between the plasmonic
properties of gold and silver nanoparticles and their size [231]–[233]. Nevertheless,
studies focusing on the effect of the various shapes of gold and silver nanoparticles on
their plasmonic properties are at their inception. For example, gold and silver
nanoparticles in spherical shape have been studied by many research groups [234], [235],
for their interesting optical and electronic properties. However, interesting plasmonic
68
properties of anisotropic plasmonic nanoparticles has caused significant interest among
researchers towards studying these types of nanoparticles recently. Gold and silver
nanoparticles in the shapes of rods, hexagons, and triangular prisms have been among a
few anisotropic structures synthesized in high yields with control over their architectural
parameters. Typically, these types of nanoparticles can be synthesized by thermal,
photochemical or electrochemistry based templates [169], [236]. Such synthesized
structures have interesting plasmonic properties in the near infrared (near-IR) and visible
regions. Generally, the method of synthesis does not seem to affect the plasmonic
properties of nanoparticles as long as their size and shape remains similar. Nanoprisms
synthesized by different methods were found to have similar physico-chemical properties
[237].
Different shapes of metal nanoparticles tend to have unique plasmonic
characteristics due to their particular geometry. In the case of triangular nanoprisms, the
interest mostly arises from the multiple absorption bands in these particles associated
with the multiple axes of their triangular shape as each of these axes can support
propagating and localized surface plasmons [238], [239]. As a result, nanoprisms, are
among the anisotropic plasmonic particles which exhibit LSPR in different orientations
depending on the polarization of the incident light. Further, triangular nanoprisms
provide us the opportunity of tuning their LSPR properties by suitably modifying their
69
structural parameters such as particle thickness, particle edge length and height [240],
[241].
Studies on various methods of triangular nanoprisms synthesis have been
performed [129], [209], [211], [237], [242]–[245]. Generally it was found that, synthetic
parameters can tune the dimensions of the nanoprisms. The typical aspect ratio (edge
length / thickness) for gold and silver triangular nanoprisms ranges from 5-40 and
depending on the synthetic procedure adopted, synthesized nanoprisms may be single
crystalline or polycrystalline. Other nanoparticle shapes such as polygons, hexagons and
circular plates have also been synthesized and reported in the literature. However, most
of the emphasis has been focused on triangular nanoprisms of gold and silver
nanoparticles which have three congruent edge lengths varying from 40 nm to one µm
and thicknesses varying from five to 50 nm [246]. The common tunable synthetic
parameters such as surfactant concentrations, metal ion and reducing agent ratios, pH,
seed particle concentration to name a few will help to tailor the nanoprism edge length,
thickness, and tip morphology, which can lead to whole new physical and chemical
properties, in particular, localized surface plasmon properties over the whole visible and
near infra-red region [237].
The dipole and quadrupole resonances in nanoprisms arise from the difference in
degree and direction of polarization of the electronic cloud relative to the incident electric
field. Thus, the optical features of gold and silver nanoprisms are largely characterized by
70
their size, shape and distribution of nanostructures in solution. It is not surprising
therefore that the frequency of the dipole and quadrupole resonant peaks shifts as the
size, shape and dielectric environment of the nanoprisms are changed. However, it is
observed that their resonant wavelengths are typically separated from each other by 100400 nm [142], [194]. The observation of dipole and quadrupole resonance at separated
wavelengths is very special for nanoprisms, as this characteristic cannot be seen in
spherical particles since the frequencies of different oscillation modes are
indistinguishable.
Despite the several advantages of triangular nanoprisms, it has been a challenge to
synthesize these nanomaterials with absolute precision in edge lengths, and corner
sharpness. Often times, synthesized triangular nanoprisms do not have the ideal sharp
corners. Instead they are synthesized with one or more truncated corners. The truncated
triangular Ag nanoprisms are more effective biocidal agents [184], [247]. Also, the
truncated triangular forms are more effective than the round or rod shaped nanoparticles
with regards to biological interactions. Zheng et al have reported the extinction efficiency
of triangular silver nanoprisms in water [142]. They concluded that truncation has
introduced blue shift and larger the truncation, higher the blue shift. Based on these
results, we got curious to see the dipole plasmonic resonance behavior upon introduction
of truncation in triangular nanoprisms of gold and silver and how they are affected by
structural features such as edge length and thickness. Addition to effect of edge length
71
and thickness, we studied the effect of introducing truncation in a sequential fashion
instead of introducing all at once in all vertices.
3.2. The effect of the edge length and thickness of perfect triangular gold and silver
nanoprism:
In order to design the hybrid nanostructure, the edge length and the thickness of
each of the Au and Ag nanoprism layers were studied individually and optimized
separately. Theoretical optimization studies were performed on a single layer of Au and
Ag nanoprism first. In this step, the nanoprism edge lengths were varied between 90-150
nm, and the thickness of each metal layer was varied between 10 nm and 30 nm in order
to optimize the thickness and the length of the layers which exhibit strong dipole
resonance. Simulation results showing the plasmonic absorbance resonance of a single
layer of Ag, and Au nanoprisms with different edge lengths and thicknesses are shown in
Figure 3.1& Figure 3.2. The simulation results shows that the plasmonic resonance of Au
and Ag nanoprisms varies as the edge length of the nanoprisms changes. Figure 3.1a
shows the FDTD simulation results for silver nanoprisms with varying edge lengths
between 90 and 150 nm each having a thickness of 30 nm. The simulation results shows
peaks characteristic of both the quadrupole and dipole resonance. Quadrupole resonance
peak observed at shorter wavelengths in comparison to dipole resonance peak. The
results demonstrates that the dipole resonance peak is the more intense peak compared to
72
the quadrupole resonance peak and this observation was independent of the edge length
of the nanoprism. Since the quadrupole peak is weak relative to the dipole peak, we have
mainly focused our study and discussion on the dipole resonant peak. As shown in Figure
3.1a, the dipole plasmonic resonance of Ag nanoprism increased from 538 nm
to 647
nm when nanoprism edge length increased from 90 nm to 150 nm. Thus dipole resonance
peak in Ag nanoprisms experienced a red shift as the edge length of the Ag nanoprism
increased. The observed red shift is due to electron accumulation in the corners of the
nanoprism and the large distance between the electrons and positive ions in the electronic
cloud of the nanoprisms which supports lower energy (i.e. longer wavelength)
oscillations [248]. In a study conducted by Millstone et al, triangular nanoprisms of Ag
and Au synthesized through nucleation approach, had exhibited a red shift in dipole
resonance peak with increase in the edge length of the prism [192]. The red shift they
observed was verified by DDA simulations too. Our observations of red shift with
increase in edge length of triangular nanoprisms of Ag and Au are in good agreement
with the report by Millstone et al. Similar to edge lengths, the intensity of dipole plasmon
resonance increased with increasing edge length in the Ag nanoprisms which is simply
due to larger number of electrons participating in the oscillations. The simulation
experiments performed for nanoprisms with edge lengths larger than 150 nm, the shift in
the dipole resonant peak becomes small as the nanoprism edge length changes. This is
due to the fact that as the length of the nanoprism becomes longer, the quantum effect on
73
the electron’s oscillation length becomes less prominent [21,22]. Thus we have limited
our investigation to nanoprisms with edge lengths of less than 150 nm. On the other hand,
simulation results show that in triangular nanoprisms with edge lengths smaller than 90
nm, the dipole peak loses its strength compared to higher order resonances (i.e.
quadrupole and higher) which limits applications for real world experiments. As a result,
edge lengths between 90 nm and 150 nm were selected for our hybrid nanoprism
structure tunability study. It is important to note that along with dipole resonance, several
higher order multiple resonance peaks were also observed for all edge lengths in our
study. However, their intensities was negligible in comparison with the dipole resonance
peak for the edge lengths we between 90 nm and 150 nm. Similar to Ag nanoprisms, the
effect of varying the edge lengths for Au nanoprisms on the plasmonic resonance peak
were also investigated (Figure 3.1b). The dimensions of Au nanoprism were maintained
exactly same as Ag nanoprism. As shown in Figure 3.1b, the plasmonic resonance of Au
nanoprism varies from 549 nm to nm to 604 nm with increasing nanoprism edge length.
Similar to the trend observed for Ag nanoprisms, the plasmonic peaks of Au nanoprism
also experienced a red shift with increase in the nanoprism edge length (Figure 3.1b).
Summary of finding are presented in Table 3.1 and Table 3.2.
74
Figure 3.1 Effect of edge length on plasmon resonance for triangular nanoprisms of a) Ag
b) Au
75
After the effect of edge length analysis, simulations were performed on
standalone Au and Ag nanoprisms to study the effect of thickness variation on the
wavelength of the dipole resonant peaks. The results of this study show that both the
position and strength of the nanoprism plasmonic peaks have a strong dependence on the
thickness of the metal layer. Figure 3.2a shows simulation results performed for Ag
nanostructures with thicknesses 10, 15, 20 and 30 nm while the edge length of the
nanoprisms were held constant at 100 nm. The plasmonic dipole resonance peaks for Ag
nanoprisms shifted from 597 nm to 705 nm when thickness decreased from 30 nm to 10
nm. Similar to silver, the effect of thickness variation in the dipole plasmonic resonance
in Au nanoprisms were investigated for the edge length of 100 nm. The thickness of Au
nanoparticles were changed between 10 nm and 30 nm. The results of the simulations
indicate that the dipole resonance peak for Au nanoparticles have experienced a blue shift
from 624 nm corresponding to the thickness of 10 nm to 566 nm corresponding to the
thickness of 30 nm (Figure 3.2b). Again, the blue shift with increase in thickness of the
nanoprism are consistent with observations made by Millstone et al for triangular
nanoprisms of Ag and Au. As the thickness of a structure with a constant edge length
increases, the structure can support higher energy oscillations in the direction
perpendicular to the edge length (i.e. the thickness), giving rise to higher energy
oscillations, which cause a blue shift in the resonance wavelength. To conclude, the
results of our study has shown that the increasing the edge length of both Ag and Au
76
nanoprism imparted a red shift in the dipole surface plasmon resonance of the nanoprisms
while increasing their thickness caused a blue shift in their dipole plasmonic resonance.
Based on the results of our simulation studies, we chose an edge length of 100 nm with a
thickness of 30 nm for Au and Ag to construct hybrid sandwich structure since they
exhibited the strongest dipole resonant peak in the visible region, which is the range of
resonance frequency with most applications.
77
Table 3.1: Effect of edge length on dipole plasmon resonance of triangular nanoprisms of
Ag and Au truncated and non-truncated
Dipole Plasmon Resonance Maximum (nm)
Edge Length (nm)
Perfect
Ag
Truncated
Ag
Perfect
Au
Truncated
Au
90 nm
538
481
549
508
100 nm
597
513
566
518
120 nm
624
549
590
543
150 nm
647
617
604
590
Table 3.2: Effect of thickness on dipole plasmon resonance of triangular nanoprisms of
Ag and Au truncated and non-truncated
Dipole Plasmon Resonance Maximum (nm)
Thickness (nm)
Perfect
Ag
Truncated
Ag
Perfect
Au
Truncated
Au
10 nm
705
549
624
548
15 nm
639
543
590
538
20 nm
617
528
578
527
30 nm
597
513
566
508
78
Figure 3.2 Effect of thickness on plasmon resonance for triangular nanoprism of (a) Ag (b) Au
79
3.2 The effect of edge length and thickness of truncated triangular gold and silver
nanoprism:
The effect of edge length and thickness for truncated nanoprisms of Au and Ag
were also investigated and compared the observations with reference to perfect
nanoprisms (Figure 3.5 & Figure 3.6) The trends were exactly the same as for nontruncated prisms of Au and Ag i.e., a red shift in dipole plasmon resonance was observed
for increase in edge length (Figure 3.3) and a blue shift is observed for increase in
thickness of nanoprism (Figure 3.4). Summary of findings are presented in Table 3.1 and
Table 3.2. The dipole plasmon resonance maximum for truncated nanoprisms of Au and
Ag occurred at lower wavelengths than the corresponding perfect prisms. Similar trends
were observed for optimization of thickness too. Truncated nanoprisms had dipole
resonance maximum at lower wavelengths when compared to perfect prism. In the same
note, perfect and truncated gold nanoprisms exhibited dipole plasmon resonance
maximum at lower wavelengths than the corresponding silver nanoprisms. As expected,
the strength of dipole plasmon resonance of Ag was observed to be more than Au.
80
Figure 3.3 Effect of edge length on plasmon resonance for truncated triangular
nanoprisms of a) Ag b) Au
81
Figure 3.4 Effect of thickness of nanoprism on plasmon resonance for truncated
triangular nanoprisms of a) Ag b) Au
82
Figure 3. 5: Comparison of effect of edge length on dipole plasmon resonance of perfect
and truncated nanoprisms of a) Ag b) Au
83
Figure 3. 6: Comparison of effect of thickness on dipole plasmon resonance of perfect
and truncated nanoprisms of a) Ag b) Au
84
3.3 The effect of truncation of gold and silver:
Ag and Au triangular nanoprisms were investigated individually for various
degree of truncation (TR) and observations were compared (Figure 3.7). TR, is defined
as a/L where a is the depth of the truncation with respect to the edge of the nanoprisms
(also called snip), and L is the edge length of the nanoprisms (100 nm) (i.e. TR= a/L =
5/100 = 0.05) as depicted in inset of the Figure 3.10 The TR values studied were 0, 0.05,
0.1, 0.2 and 0.25, which corresponds to the snips: a = 0, 5, 10, 20 and 25 nm, respectively
for the edge length of 100 nm (Table 3.3). The plasmonic resonance of Ag and Au
nanoprisms were presented in Figure 3.10. The perfect nanoprism with no truncation had
dipole resonance peak at 579 nm (for Ag nanoprisms) and 566 nm (for Au nanoprisms).
Introduction of snipping (TR = 0.05) to the nanoprisms causes a significant blue shift for
the dipole plasmon resonance of both Au and Ag nanoprisms [251]. For Ag nanoprisms a
30nm blue shift in the plasmonic peak was observed which was from 579 nm (TR = 0) to
549 nm (TR = 0.05). Similarly for Au nanoprisms, a blue shift of 20 nm was observed
i.e., from 566 nm (TR = 0) to 546 nm (TR = 0.05); which is a relatively smaller shift
compared to Ag nanoprisms. This blue shift effect in the truncated nanoprisms occurs
because the length of the quantum box for electron oscillation is smaller in the truncated
nanoprisms (Figure 3.10A). In addition, the electron density in the corners of a
nanoparticle plays an important role in determining the resonant wavelength [252] and
this blue shift effect is partly attributed to the lower electronic density in the corners as
85
they are snipped away. The blue shift continued as the truncation of the corners of the
nanoprisms become deeper for both Ag and Au nanoprisms
86
Figure 3.7. Comparison of Ag and Au triangular nanoprisms for change in dipole
plasmon resonance with variation in degree of truncation.
87
Upon introduction of truncation, the strength of dipole plasmon resonance peak
dropped significantly for both gold and silver (Figure 3.10B). This result is to be
expected as by introducing the snip to the nanostructure, we have effectively removed the
accumulation of free electrons at the corners which play an important role in supporting
the plasmonic resonance causing a decrease in the strength of plasmonic oscillations (also
known as the “lightning rod effect”) [253]. The strength of the signal kept dropping with
increase in truncation for Ag nanoprisms. For Au nanoprism, the drop in strength of the
dipole resonance peak was extended only until truncation of 0.1. Additional increase in
truncation does not result in drop of the strength of the signal, instead, they fairly
remained constant.
Initially, we studied the effect of various depths of truncation in an Ag nanoprism
with only one truncated corner. Figure 3.8 is an illustration of the effects of various
depths of corner truncations in the Ag nanoprism with edge length of 150 nm. Increasing
the depth of corner truncation in the Ag nanoprism causes a plasmonic blue shift from
764 nm for the case of no truncation (TR=0) to 696 nm for the case of a truncation depth
of 20 nm (TR= 0.13). Further the intensity of dipole plasmon resonance of untruncated
triangular nanoprism is smaller than the truncated nanoprisms. The enhancement in the
signal intensity of truncated nanoprisms might be due to “lightning rod effect”.
88
Figure 3.8. Effect of degree of truncation at only one vertex of Ag nanoprism on dipole
plasmon resonance.
89
Figure 3.9. Plasmonic resonance of triangular Ag nanoprisms with truncation in one, two,
and three vertices (A) wavelength position of the peaks. (B) absorbance strength of the
peaks [251].
90
Next, we studied Ag triangular nanoprism with two and three truncated corners to
determine the effect of the number of truncated corners on the plasmonic resonance shift
and the strength of the plasmonic peaks. Ag nanoprisms were investigated for various TR
values for one, two, or three truncated corners. These TR values were 0.05, 0.1, and 0.15,
which corresponded to the snips: a = 5, 10, and 15 nm, respectively for a nanoprism with
edge length of 150 nm. Figure 3.9A presents the absorbance of Ag nanoprisms with no
truncated corners as well as truncated Ag nanoprisms with one, two or all three truncated
corners with various degrees of truncation. Simulation results showed that removing one,
two, or three tips of triangular nanoprism up to 15 nm of truncation depth has no effect on
the position of the dipole plasmon peak (Figure 3.9A) or the strength of Ag nanoprisms
(Figure 3.9B). It is important to note that the blue shifting of the resonant wavelengths
continue as increase the depth of truncation. However, the resonance strength maximizes
at TR=0.02 and drops as we increase the truncation depth.
The full width at half maximum (FWHM) for Ag and Au plasmonic peaks were
measured for the TR values mentioned previously and tabulated in Table 3.4. The
FWHM has decreased with increase in TR values for both Au and Ag resulting in
narrower peaks.
91
Table 3.3: Effect of truncation on dipole plasmon resonance of triangular nanoprisms of
Ag and Au
Degree of Truncation
Dipole Plasmon Resonance Maximum
Ag
Au
0
597
566
0.05
549
554
0.1
512
527
0.15
490
517
0.2
472
512
0.25
464
503
Table 3.4: Full Width Half Maximum of dipole plasmon resonance of truncated
triangular nanoprisms of Ag and Au
Degree of Truncation
Full Width at Half Maximum (FWHM)
Ag (nm)
Au (nm)
0
48.35
53.54
0.05
47.06
44.27
0.1
45.59
42.54
0.2
43.38
41.26
92
Figure 3.10 FDTD simulation results showing the plasmonic resonance of nanoprism that
has thickness of 30 nm and edge length of 100 nm with different degrees of truncation for
(A) Ag. (B) Au.
93
The plasmonic enhancements for Ag nanoprisms with and without truncation
were investigated.
In Figure 3.11 (a-b) is ideal triangular Ag nanoprism without
truncation, while Figure 3.11 (c-d) a snip of 10 nm was introduced. For Figure 3.11(a-d)
the thickness and edge length were 30 nm and 100 nm respectively. In Figure 3.11 a and
c the incident light is perpendicular to the polarization plane, whereas, for Figure 3.11 b
and d the incident light is parallel to the polarization place. The enhancement factor =
(|E|²in the presence of prism)/(|E|2 in the absence) was found to be significantly higher in
ideal triangular nanoprism than for the nanoprism with snipping.
Further for both
triangular nanoprisms with and without snipping, enhancement was very significant when
incident light was perpendicular to the polarization plane than parallel to polarization
plane. The enhancement factors calculated for the prisms in Figure 3.11 (a-d) are 4.75,
3.88, 1.92 and 0.8 respectively. The reason for higher plasmonic enhancement in
triangular silver nanoprism without snipping was due to “lightning rod effect” as the
edges are sharper in this case than the truncated nanoprism.
94
a
b
c
d
Figure 3.11 The plasmonic enhancement of Ag nanoprism without snipping (a and b) and
truncated nanoprism (c and d) with snip of 10 nm. The edge length (100 nm) and
thickness (30nm) were maintained constant in above figure (a – d).
95
Figure 3.12 The plasmonic enhancement of Au nanoprism without snipping (a and b) and
truncated nanoprism (c and d) with snip of 10 nm. The edge length (100 nm) and
thickness (30nm) were maintained constant in above figure (a – d).
96
3.4 CONCLUSIONS
Finite-difference time-domain (FDTD) simulations, were performed on triangular
nanoprisms of Au and Ag for perfect and truncated nanoprisms to understand the role of
structural parameters such as edge length, thickness, and truncation. Increasing the edge
length of triangular nanoprisms of Au and Ag truncated and non-truncated had introduced
a red shift while, the increase in thickness had introduced a blue shift. The dipole
plasmon resonance maximum occurred at lower wavelengths for Au gold nanoprisms
than Ag. Similarly, the dipole plasmon resonance of truncated nanoprism occurred at
lower wavelengths than the non-truncated prism. The strength of dipole plasmon
resonance silver nanoprisms are higher than gold as it had least losses.
97
Chapter 4
The Effect of Truncation and Dielectric in Plasmonic Resonance of Hybrid
Plasmonic Nanosandwich Structures in Optical Range
4.1 Introduction:
Since the days scientists found the strong absorption band of gold nanoparticle in
the visible region, noble metal nanoparticles had been a great subject of investigation
[32], [254], Thus observed strong absorption band of gold was explained by Mie through
finding solutions for Maxwell’s equations using suitable boundary settings. The material
related functions found in Mie’s theory are dielectric function of the metal and
surrounding medium’s dielectric constant. Surrounding medium also known as capping
material, plays a crucial role in plasmonic properties exhibited by nanomaterials as it
prevents aggregation prevailing during the synthesis conditions[255], [256], The
absorption spectra of metal nanoparticles and its strength are intertwined with refractive
index of the surroundings. Thus the sensitivity of nanoparticles to refractive index has
opened new avenue of study called biosensors [257]–[259].
Metal nanoparticles coupled to target molecule receptors have surface plasmon
properties shifted, curbed or enriched in presence of target molecules. The degree of
98
response by nanoparticles to target molecules depends on thickness of refractive index
and sensitivity of dipole plasmon resonance to changes in bulk environment’s refractive
index. Several research groups are actively pursuing studies experimentally as well as
theoretically to understand the surface plasmon resonance dependence to bulk and local
refractive index and several reports were already published towards that direction [146],
[260]–[262]. The general observation on articles published was, dipole plasmon
resonance had a red shift with increase in refractive index for a range of nanoparticle
shapes [263], [264]. Further, the magnitude of sensitivities depends on shape, size and
composition of nanoparticles. Owing the reasons described in the introduction of the
dissertation, we pursued the FDTD simulations to understand the effect of refractive
index sensitivity in triangular nanoprisms of gold and silver. Effect of surrounding
medium refractive medium and its impact on surface plasmon resonance are abundant
[265], [266]. For single silver nanoparticles, the change in surface plasmon resonance
were studied by addition and removal of oil surrounding it. The color of silver
nanoparticles changed from blue to green with addition of oil indicating a red shift and
the color were reverted to blue by removing the oil [267]. Van Duyne, studied the
scattering of single silver nanoparticles dispersed in solvents such as ethanol, nitrogen, npropanol, benzene and chloroform [268]. Increase in dielectric constant of medium
produced a linear increase in red shift of dipole plasmon resonance maximum. In another
study, gold nanoparticles with different shapes and surface modifications were studied.
99
Between spherical, triangular and rod-like particles, rods exhibited more sensitivity to
surrounding medium and this observation was in direct correlation to aspect ratio of the
material investigated.
Hybrid nanoprisms which take advantage of two different noble metals in their
structures have become increasingly important as they can combine plasmonic dipole
peaks associated with gold as well as silver, and thereby create additional dipole
plasmonic peaks which have a higher intensity level. The additional peaks can provide a
higher degree of control over the tunability of nanoprism resonance and can potentially
be beneficial in various applications [178], [269]. With that in mind, in this paper, we
introduce a simple hybrid nanoprism structure consisting of Au and Ag metallic
nanoprisms layers separated by a dielectric layer.
4.2 The effect of dielectric:
The effect of adding a dielectric layer to either Ag or Au metal layers on dipole
plasmon resonance was investigated. Addition of dielectric layer to Au or Ag metal
layers facilitates the shift of dipole plasmonic resonant peak even further and tune the
plasmonic properties of the nanoprisms at will. Ag nanoprism with edge length of 100
nm and thicknesses of 30 nm were chosen for investigation to understand the role of
dielectric. The thickness of the dielectric layer was varied between 10 nm and 60 nm. For
each dielectric thickness, refractive index values from 1 to 3 were thoroughly analyzed.
100
Table 4.1: Summary of results investigated for effect of dielectric thickness for various
refractive indices on dipole plasmon resonance
Dipole plasmon resonance maximum of Ag dielectric sandwich
Refractive
for thickness (nm)
index
10
30
50
70
90
1
610
610
610
610
610
1.5
632
654
662
662
662
2
646
670
679
679
679
2.5
687
724
733
743
743
3
705
786
809
812
812
Table 4.2: Summary of results investigated for effect of dielectric thickness for various
refractive indices on dipole plasmon resonance
Refractive
Dipole plasmon resonance maximum of Au dielectric sandwich
index
for thickness (nm)
10
30
50
70
90
1
572
572
572
572
572
1.5
590
597
603
603
603
2
604
610
617
624
624
2.5
624
638
646
654
654
3
639
670
678
687
687
101
Silver nanoprism coupled with dielectric thickness of 10 nm, the dipole plasmon
resonance maximum of the sandwich had a red shift when refractive index changed from
1 to 3 (Figure 4.1). Summary of results were presented in Table 4.1 and Figure 4.3. For
refractive index value of 1, 1.5, 2, 2.5 and 3 nm the dipole plasmon resonance maximum
was 610, 632, 660, 687, and 705 nm respectively. Similar red shift was observed for
dielectric thickness of 30, 50, 70, and 90 nm respectively. For refractive index of 1, no
change in dipole plasmon resonance wavelength was observed when thickness changed
10 nm to 90 nm. However, for the refractive index of 1.5, 2, 2.5, and 3 dipole plasmon
resonance maximum found a red shift with increase in thickness of dielectric.
Interestingly, the magnitude of red shift has increased with increase in the refractive
index for the thickness of dielectric investigated. Thus, the magnitude of dipole plasmon
resonance shift for the refractive indices of 1, 1.5, 2, 2.5 and 3 are 0, 30, 33, 56 and 107
nm respectively for the variation of dielectric thickness. Additionally, the observed red
shift for a given refractive index was observed only for variation in thickness of dielectric
from 10 nm to 50 nm only. For all the refractive indices investigated, when dielectric
thickness changed from 50 nm to 90 nm, the wavelength of dipole plasmon resonance
remained constant. Further, for a nanoprism with similar dimensions and refractive index
of 1.5 without the dielectric had dipole plasmon resonance maximum at lower
wavelength than the nanoprism with dielectric. Similar to the observations made for Ag,
102
Au nanoprism also exhibited exactly the same trend for change in dielectric thickness
with respect to refractive index (Figure 4.2). The results are summarized in Table 4.2 and
Figure 4.3. The only difference observed was, the magnitude of red shift was relatively
lower for Au than Ag (Figure 4.4).
103
Figure 4.1 FDTD simulation results showing the absorbance spectra of Ag nanosandwich
structures with edge length of 100 nm and thickness 30 nm. This figure of for dielectric
thickness of 50 nm.
104
Figure 4.2 FDTD simulation results showing the absorbance spectra of Au nanosandwich
structures with edge length of 100 nm and thickness 30 nm. This figure of for dielectric
thickness of 50 nm.
105
Figure 4.3: Effect of refractive index on dipole plasmon resonance maximum for various
thicknesses of dielectric of a) Ag b) Au
106
Figure 4.4: Comparison of dipole resonance maximum for Ag and Au towards change in
dielectric medium with thickness of 30 nm.
107
Figure 4.5. FDTD Simulation results showing the plasmonic resonance of Au and Ag
nanoprism with edge length of 100 nm and thickness of 30 nm and FDTD Simulation
results showing the plasmonic resonance of an Au- dielectric-Ag nanoprism with edge
length of 100 nm and thickness of 30 nm for all layers. (solid black line), ( A: edge
length, B: height, and C: thickness) .
108
The hybrid nano-sandwich structure studied in this paper consists of three
material layers namely a silver layer, a dielectric separating layer, and a gold layer
(Figure 4.5, inset). As described above, plasmonic properties of the nanoprisms strongly
depend on their shape and size as well as their material properties. To show the advantage
of using a three-layered nanoprism, we have constructed the triangular nanoprism as
explained above using OptiFDTD software. A single layer of Au or Ag nanoprism can
only support a single dipole plasmonic resonance. This resonant peak occurs at ~646 nm
for an Au nanoprism with an edge length of 100 nm and a thickness of 30 nm while it
occurs at ~815 nm for an Ag nanoprism of the same size and shape (Figure 4.5). In
contrast, a hybrid nanoprism made with a layer of Au and a layer of Ag in addition to a
silica separating dielectric layer of 30 nm thick can support two dipole plasmonic peaks
as illustrated in Figure 4.5.
109
4.3 Ag-dielectric-Au Sandwich:
Bi-metallic triangular nanosandwich was constructed with Au and Ag using silica
as dielectric layer with an aim to extend the scope of investigation beyond individual
metallic triangular nanoprisms for tuning the plasmonic properties. Tuning the plasmonic
properties of triangular nanoprism sandwiches helps us to tailor materials for need based
specific applications. The edge length of dielectric and metal was chosen 100 nm and
thickness of Ag and Au 30 nm. The thickness of dielectric layer was changed between 5
nm to 100 nm.
The reason for adding dielectric between Ag and Au is to enhance tunability of
the sandwich structure. The plasmonic peak of the entire structure can be tweaked just by
changing the thickness of the dielectric separating layer [270].
As previously stated, the advantage of constructing an Ag-dielectric-Au sandwich
structure is the ability to tune the wavelength of the two plasmonic peaks in addition to
the relative strength of the two peaks with respect to each other.
The hybrid Ag-dielectric-Au nanoprism sandwich was constructed with edge
length of 100 nm for Au, Ag and dielectric and thickness of Ag and Au are 30 nm in the
simulation study is a structure as described above. The refractive index of the dielectric
layer was 1.5.
The findings of the simulation study for the above constructed sandwich as
follows: as the thickness of dielectric layer changed in the sandwich nanoprism structure,
110
the strength of the two plasmonic peaks with respect to each other changed as well. For
the sandwich structure, with a dielectric layer of 5 nm thickness, the plasmonic peak due
to Ag is much stronger than the plasmonic peak due to Au (Figure 4.6A). However,
when the thickness of the dielectric layer increased from 5 nm to 20 nm dipole plasmon
resonance peak of Au increased significantly, yet the intensity of Ag nanoprism was
stronger relatively. When the thickness of the dielectric layer was further increased to 30
nm, the strength of the peaks due to Ag and Au became almost equal. Further increase in
the dielectric layer thickness to 60 nm and 100 nm caused the dipole resonant peak due to
Au become more intense in comparison with the Ag peak (Figure 4.6A). The intensities
of dipole plasmon resonance peak of Ag and Au for perfect and truncated sandwich was
presented in It is very evident that dipole plasmon resonance of Ag is always more
intense than Au due to less radiative losses. However, for the dielectric thickness of 60
nm and 100 nm the dipole plasmon resonance peak of Au was observed to be more
intense than Ag. This observation requires further investigation.
Next, truncation was introduced to the nanosandwich structure. The degree of
truncation of the nanosandwich structure was chosen as
The edge length of the nanosandwich is fixed at 100 nm. Our simulation results indicate
that both Au and Ag plasmonic peaks in the sandwich structure experienced a blue shift
111
upon introduction of truncation (Figure 4.6B). This is consistent with our previous
observations made for the truncated standalone Au and Ag nanoprisms. Further we have
observed a reduction in the distance between the two peaks in the truncated
nanosandwich structure. This reduction is due to the fact that Ag plasmonic peak which is
located at longer wavelengths, generally experiences a larger blue shift compared to the
Au plasmonic peak as truncation is introduced to the structure causing the distance
between the two peaks to decrease. The blue shift of two plasmonic peaks bring both Au
and Ag peaks of the nanosandwich structure within the visible range which is ideal for
many biological, medical and electronic applications. Further, similar to the single metal
layer nanoprism, introduction of truncation to the nanosandwich structure causes a
narrowing in the FWHM of the plasmonic peaks. This narrowing is due to the fact that
shortening the edge length of the structure reduces the number of resonances supported
by the structure at each length causing a narrowing the range of resonance energies.
Additionally, we have two peaks in the sandwich structures we constructed. The
advantage of having two plasmonic peaks will help us to design materials that are capable
of sensing multiple analytes. Further the applications of these sandwich structures can be
used in up conversion of phosphors and plasmonic enhancement of fluorescent materials.
For fluorescent materials, one peak enhances the emission rate and other one enhances
the absorption rate. Interestingly, having two peaks avoids the use of mixture of
triangular nanoprisms with different edge lengths to sense two different analytes. Further,
112
for analysis that involves triangular nanoprisms in closer proximity, might pose a
challenge. Those challenges are well addressed via sandwich structures.
113
Figure 4.6 (a) FDTD simulation results showing the absorbance of sandwich structure
(Au/dielectric/Ag) (a) without truncation and (b) with TR= 0.1 (First peak is
corresponding to Au & Second peak is corresponding to Ag) [271].
114
Figure 4.7: Relationship between the magnitude of Ag and Au peaks and varying
thickness of dielectric layer (nm) (A) Perfect sandwich structure and (B) Truncated
sandwich structure
115
4.4 Conclusion:
In this chapter, we have investigated effect of dielectric on dipole plasmon
resonance when coupled with Au and Ag. Addition of dielectric has increased the
wavelength at which dipole plasmon resonance occurs. Further, when the thickness of
dielectric layer was increased red shift was observed. Additionally, the magnitude of red
shift was increased with increase in refractive index medium. Next we constructed the
hybrid nanoprism structures truncated and non-truncated exhibited two dipole plasmonic
peaks in the visible frequency range which can be tuned by changing the thickness of the
dielectric layer which effects both the strength of each of the peak as well as the
wavelength position of the peak. Our simulations show high level of control on the
tunability of these parameters which can be beneficial in various applications.
116
Chapter 5
Conclusions and Future Work
In this thesis, we have presented state of the art techniques available to synthesize
anisotropic triangular nanoprisms. Further we have constructed the triangular nanoprisms
of gold and silver and studied the effect of structural parameters such as edge length,
thickness, truncation and dielectric on plasmonic properties using FDTD simulations.
FDTD simulations revealed that increasing the edge length of both Au and Ag
nanoprisms introduced a red shift, while increasing the thickness introduced a blue shift,
it was conversely noted that the dipole plasmon resonance maximum occurred at lower
wavelengths for Au than for Ag. Similarly, the dipole plasmon resonance of the truncated
nanoprisms occurred at lower wavelengths than for the non-truncated nanoprisms.
Furthermore, the strength of the dipole plasmon resonance of the Ag nanoprisms was
higher than for the Au nanoprisms, as Ag showed the least losses.
The addition of dielectric increased the wavelength at which dipole plasmon
resonance occurred. When the thickness of the dielectric layer was increased, a red shift
was observed. It was also noted that the magnitude of the red shift was increased with a
corresponding increase in the refractive index medium. Finally, we constructed the
hybrid nanoprism structures, truncated and non-truncated. This study exhibited two
117
dipole plasmonic peaks in the visible frequency range that could be tuned by changing
the thickness of the dielectric layer. This change affected both the strength of each peak
as well as the wavelength position of the peak. This investigation showed a high level of
control on the tunability of the established parameters that can be useful in various
applications. The preliminary results we obtained through FDTD simulations will
encourage future researchers to construct triangular nanoprism sandwich structures to
take advantage of all the surface plasmon features we observed.
While the results from FDTD simulations are very promising and motivating to
investigate it experimentally, it would be appropriate to remember that FDTD requires
that the entire computational domain be gridded, and the grid spatial discretization must
be sufficiently fine to resolve both the smallest electromagnetic wavelength and the
smallest geometrical feature in the model, very large computational domains can be
developed, which results in very long solution times. Models with long, thin features,
(like wires) are difficult to model in FDTD because of the excessively large
computational domain required.
118
References
[1]
D. N. Adrian Huber, Salvatore Demartis, “The use of biosensor technology for the
engineering of antibodies and enzymes,” J. Mol. Recognit., vol. 12, no. 3, pp. 198–
216, 1999.
[2]
M. N. Weiss, R. Srivastava, H. Groger, P. Lo, and S.-F. Luo, “A theoretical
investigation of environmental monitoring using surface plasmon resonance
waveguide sensors,” Sensors Actuators A Phys., vol. 51, no. 2–3, pp. 211–217,
Nov. 1995.
[3]
D. SHANKARAN, K. GOBI, and N. MIURA, “Recent advancements in surface
plasmon resonance immunosensors for detection of small molecules of biomedical,
food and environmental interest,” Sensors Actuators B Chem., vol. 121, no. 1, pp.
158–177, Jan. 2007.
[4]
J. Homola, Surface Plasmon Resonance Based Sensors, vol. 4. Berlin, Heidelberg:
Springer Berlin Heidelberg, 2006.
[5]
J. Homola, “Surface Plasmon Resonance Sensors for Detection of Chemical and
Biological Species,” Chem. Rev., vol. 108, no. 2, pp. 462–493, Feb. 2008.
[6]
G. G. Nenninger, M. Piliarik, and J. Homola, “Data analysis for optical sensors
based on spectroscopy of surface plasmons,” Meas. Sci. Technol., vol. 13, no. 12,
pp. 2038–2046, Dec. 2002.
[7]
R. Karlsson and A. Fält, “Experimental design for kinetic analysis of proteinprotein interactions with surface plasmon resonance biosensors,” J. Immunol.
Methods, vol. 200, no. 1–2, pp. 121–133, Jan. 1997.
[8]
J. Dostálek and J. Homola, “Surface plasmon resonance sensor based on an array
of diffraction gratings for highly parallelized observation of biomolecular
interactions,” Sensors Actuators B Chem., vol. 129, no. 1, pp. 303–310, Jan. 2008.
[9]
J. T. Hastings, J. Guo, P. D. Keathley, P. B. Kumaresh, Y. Wei, S. Law, and L. G.
Bachas, “Optimal self-referenced sensing using long- and short- range surface
plasmons,” Opt. Express, vol. 15, no. 26, p. 17661, 2007.
[10] U. Kreibig and M. Vollmer, Optical Properties of Metal Clusters. Springer
119
Science & Business Media, 2013.
[11] P. K. Jain, K. S. Lee, I. H. El-Sayed, and M. A. El-Sayed, “Calculated Absorption
and Scattering Properties of Gold Nanoparticles of Different Size, Shape, and
Composition: Applications in Biological Imaging and Biomedicine,” J. Phys.
Chem. B, vol. 110, no. 14, pp. 7238–7248, Apr. 2006.
[12] M. A. van Dijk, M. Lippitz, and M. Orrit, “Far-Field Optical Microscopy of Single
Metal Nanoparticles,” Acc. Chem. Res., vol. 38, no. 7, pp. 594–601, Jul. 2005.
[13] L. R. Hirsch, R. J. Stafford, J. A. Bankson, S. R. Sershen, B. Rivera, R. E. Price, J.
D. Hazle, N. J. Halas, and J. L. West, “Nanoshell-mediated near-infrared thermal
therapy of tumors under magnetic resonance guidance,” Proc. Natl. Acad. Sci., vol.
100, no. 23, pp. 13549–13554, Nov. 2003.
[14] I. H. El-Sayed, X. Huang, and M. A. El-Sayed, “Surface Plasmon Resonance
Scattering and Absorption of anti-EGFR Antibody Conjugated Gold Nanoparticles
in Cancer Diagnostics: Applications in Oral Cancer,” Nano Lett., vol. 5, no. 5, pp.
829–834, May 2005.
[15] I. ELSAYED, X. HUANG, and M. ELSAYED, “Selective laser photo-thermal
therapy of epithelial carcinoma using anti-EGFR antibody conjugated gold
nanoparticles,” Cancer Lett., vol. 239, no. 1, pp. 129–135, Jul. 2006.
[16] C. Loo, A. Lowery, N. Halas, J. West, and R. Drezek, “Immunotargeted
Nanoshells for Integrated Cancer Imaging and Therapy,” Nano Lett., vol. 5, no. 4,
pp. 709–711, Apr. 2005.
[17] K. M. Mayer and J. H. Hafner, “Localized surface plasmon resonance sensors,”
Chem. Rev., vol. 111, no. 6, pp. 3828–3857, 2011.
[18] F. Tam, C. Moran, and N. Halas, “Geometrical Parameters Controlling Sensitivity
of Nanoshell Plasmon Resonances to Changes in Dielectric Environment,” J. Phys.
Chem. B, vol. 108, no. 45, pp. 17290–17294, Nov. 2004.
[19] S. Link, Z. L. Wang, and M. A. El-Sayed, “Alloy Formation of Gold−Silver
Nanoparticles and the Dependence of the Plasmon Absorption on Their
Composition,” J. Phys. Chem. B, vol. 103, no. 18, pp. 3529–3533, May 1999.
[20] G. Raschke, S. Brogl, A. S. Susha, A. L. Rogach, T. A. Klar, J. Feldmann, B.
Fieres, N. Petkov, T. Bein, A. Nichtl, and K. Kürzinger, “Gold Nanoshells
Improve Single Nanoparticle Molecular Sensors,” Nano Lett., vol. 4, no. 10, pp.
1853–1857, Oct. 2004.
[21] D. Compton, L. Comish, and E. van der Lingen, “The third order nonlinear optical
properties of gold nanoparticles in glasses, part I,” Gold Bull., vol. 36, no. 10–16,
pp. 51–58, 2003.
120
[22] K. Kalishwaralal, V. Deepak, S. Ram Kumar Pandian, M. Kottaisamy, S.
BarathManiKanth, B. Kartikeyan, and S. Gurunathan, “Biosynthesis of silver and
gold nanoparticles using Brevibacterium casei,” Colloids Surfaces B Biointerfaces,
vol. 77, no. 2, pp. 257–262, 2010.
[23] F. Antonii, “‘Panacea aurea-auro potabile.,’” Hambg. Ex Bibliopolio Frobeniano,
p. 250, 1618.
[24] R. Kahn, “Serum Diagnosis for Syphilis.,” Colloid Chem., vol. 2, p. 757, 1928.
[25] E. A. Hauser, “Aurum potabile,” J. Chem. Educ., vol. 29, no. 9, p. 456, Sep. 1952.
[26] D. H. Brown and W. E. Smith, “The chemistry of the gold drugs used in the
treatment of rheumatoid arthritis,” Chem. Soc. Rev., vol. 9, no. 2, p. 217, 1980.
[27] A. D. Hyatt and B. Eaton, Immuno-gold electron microscopy in virus diagnosis
and research. CRC Press, 1992.
[28] M. Faraday, “The Bakerian Lecture: Experimental Relations of Gold (and Other
Metals) to Light,” Philos. Trans. R. Soc. London, vol. 147, pp. 145–181, 1857.
[29] The Royal Institution’s Faraday Museum, The Royal Institution of Great Britain.
London, UK.: 21 Albemarle Street.
[30] W. Ostwald, “Zur Geschichte des Colloiden Goldes.,” Kolloid Polym. Sci., vol. 4,
no. 1, pp. 5–14, 1909.
[31] C. Cretu and E. Van Der Lingen, “Coloured Gold Alloys,” Gold Bull., vol. 32, no.
September, pp. 115–126, 1999.
[32] G. Mie, “Beiträge zur Optik trüber Medien, speziell kolloidaler Metallösungen,”
Ann. Phys., vol. 25, no. 3, pp. 377–445, 1908.
[33] M. Kerker, The Scattering of Light and other Electromagnetic Radiation.
Academic Press: New York, 1969.
[34] W. Hergert and T. Wriedt, The Mie Theory, vol. 169. 2012.
[35] R. Feynman, “Miniaturization,” Reinhold, New York, pp. 282–296, 1961.
[36] “Gold Nanoparticles: Properties and Applications | Sigma-Aldrich.” [Online].
Available: https://www.sigmaaldrich.com/materials-science/nanomaterials/goldnanoparticles.html. [Accessed: 24-Apr-2016].
[37] U. Kreibig and M. Vollmer, Optical Properties of Metal Clusters. Springer
Science \& Business Media, 2013.
[38] G. Schmid, Clusters and Colloids - From Theory to Applications. VCH:
Weinheim, Germany, 1994.
[39] C. Brechignac, P. Houdy, and M. Lahmani, Nanomaterials and nanochemistry.
121
2007.
[40] H. A. Atwater, “The Promise of Plasmonics,” Sci. Am., vol. 296, no. 4, pp. 56–62,
Apr. 2007.
[41] S. K. Ghosh, A. Pal, S. Kundu, S. Nath, and T. Pal, “Fluorescence quenching of 1methylaminopyrene near gold nanoparticles: size regime dependence of the small
metallic particles,” Chem. Phys. Lett., vol. 395, no. 4–6, pp. 366–372, Sep. 2004.
[42] S. K. Ghosh, S. Kundu, M. Mandal, and T. Pal, “Silver and Gold Nanocluster
Catalyzed Reduction of Methylene Blue by Arsine in a Micellar Medium,”
Langmuir, vol. 18, no. 23, pp. 8756–8760, Nov. 2002.
[43] R. Kubo, “Electronic Properties of Metallic Fine Particles. I.,” J. Phys. Soc. Japan,
vol. 17, no. 6, pp. 975–986, 1962.
[44] P. R. Sajanlal, T. S. Sreeprasad, A. K. Samal, and T. Pradeep, “Anisotropic
nanomaterials: structure, growth, assembly, and functions,” Nano Rev., vol. 2, no.
0, pp. 1–62, 2011.
[45] S. Chen and R. Pei, “Ion-Induced Rectification of Nanoparticle Quantized
Capacitance Charging in Aqueous Solutions,” J. Am. Chem. Soc., vol. 123, no. 43,
pp. 10607–10615, Oct. 2001.
[46] A. Henglein and M. Giersig, “Optical and Chemical Observations on
Gold−Mercury Nanoparticles in Aqueous Solution,” J. Phys. Chem. B, vol. 104,
no. 21, pp. 5056–5060, Jun. 2000.
[47] S. Park, P. Yang, P. Corredor, and M. J. Weaver, “Transition Metal-Coated
Nanoparticle Films: Vibrational Characterization with Surface-Enhanced Raman
Scattering,” J. Am. Chem. Soc., vol. 124, no. 11, pp. 2428–2429, Mar. 2002.
[48] J.-I. Park and J. Cheon, “Synthesis of ‘Solid Solution’ and ‘Core-Shell’ Type
Cobalt−Platinum Magnetic Nanoparticles via Transmetalation Reactions,” J. Am.
Chem. Soc., vol. 123, no. 24, pp. 5743–5746, Jun. 2001.
[49] Z. L. Wang, “Transmission Electron Microscopy of Shape-Controlled
Nanocrystals and Their Assemblies,” J. Phys. Chem. B, vol. 104, no. 6, pp. 1153–
1175, Feb. 2000.
[50] J. T. Krug, G. D. Wang, S. R. Emory, and S. Nie, “Efficient Raman Enhancement
and Intermittent Light Emission Observed in Single Gold Nanocrystals,” J. Am.
Chem. Soc., vol. 121, no. 39, pp. 9208–9214, Oct. 1999.
[51] A. C. Templeton, M. J. Hostetler, E. K. Warmoth, S. Chen, C. M. Hartshorn, V.
M. Krishnamurthy, M. D. E. Forbes, and R. W. Murray, “Gateway Reactions to
Diverse, Polyfunctional Monolayer-Protected Gold Clusters,” J. Am. Chem. Soc.,
vol. 120, no. 19, pp. 4845–4849, May 1998.
122
[52] M. P. Pileni, A. Taleb, and C. Petit, “Silver metal nanosized particles: Control of
particle size, self assemblies in 2D and 3D superlattices and optical properties,” J.
Dispers. Sci. Technol., vol. 19, no. 2–3, pp. 185–206, Jan. 1998.
[53] A. Henglein, “Colloidal Palladium Nanoparticles: Reduction of Pd(II) by H 2 ; Pd
C ore Au S hell Ag S hell Particles,” J. Phys. Chem. B, vol. 104, no. 29, pp. 6683–
6685, Jul. 2000.
[54] M. M. Alvarez, J. T. Khoury, T. G. Schaaff, M. N. Shafigullin, R. L. Whetten, and
I. Vezmar, “Optical Absorption Spectra of Nanocrystal Gold Molecules,” J. Phys.
Chem. B, vol. 101, no. 19, pp. 3706–3712, 1997.
[55] Y. Li, C. Jing, L. Zhang, and Y.-T. Long, “Resonance scattering particles as
biological nanosensors in vitro and in vivo.,” Chem. Soc. Rev., vol. 41, no. 2, pp.
632–42, Jan. 2012.
[56] R. H. Ritchie, “Plasma Losses by Fast Electrons in Thin Films,” Phys. Rev., vol.
106, no. 5, pp. 874–881, 1957.
[57] H. Raether, “Surface-Plasmons on Smooth and Rough Surfaces and on Gratings,”
Springer Tracts in Modern Physics, vol. 111. pp. 1–133, 1988.
[58] H. Raether, Surface Plasmons ed G Hohler. Berlin: Springer, 1988.
[59] W. L. Barnes, A. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength
optics.,” Nature, vol. 424, no. 6950, pp. 824–30, Aug. 2003.
[60] M. Moskovits, “Surface-enhanced spectroscopy,” Rev. Mod. Phys., vol. 57, no. 3,
pp. 783–826, Jul. 1985.
[61] H. Metiu and P. Das, “The Electromagnetic Theory of Surface Enhanced
Spectroscopy,” Annu. Rev. Phys. Chem., vol. 35, no. 1, pp. 507–536, Oct. 1984.
[62] W. L. Barnes, a. Dereux, and T. W. Ebbesen, “Surface plasmon subwavelength
optics,” Nature, vol. 424, no. 6950, pp. 824–30, 2003.
[63] R. W. Wood, “XLII. On a remarkable case of uneven distribution of light in a
diffraction grating spectrum,” Philos. Mag. Ser. 6, vol. 4, no. 21, pp. 396–402,
Sep. 1902.
[64] U. FANO, “The Theory of Anomalous Diffraction Gratings and of QuasiStationary Waves on Metallic Surfaces (Sommerfeld’s Waves),” J. Opt. Soc. Am.,
vol. 31, no. 3, p. 213, Mar. 1941.
[65] A. Otto, “Excitation of nonradiative surface plasma waves in silver by the method
of frustrated total reflection,” Zeitschrift f�r Phys., vol. 216, no. 4, pp. 398–410,
Aug. 1968.
[66] E. Kretschmann and H. Raether, “Notizen: Radiative Decay of Non Radiative
123
Surface Plasmons Excited by Light,” Zeitschrift für Naturforsch. A, vol. 23, no. 12,
pp. 2135–2136, Jan. 1968.
[67] A. D. Boardman, Electromagnetic Surface Modes. Chichester, UK: Wiley, 1980.
[68] A. Ishimaru, S. Jaruwatanadilok, and Y. Kuga, “GENERALIZED SURFACE
PLASMON RESONANCE SENSORS USING METAMATERIALS AND
NEGATIVE INDEX MATERIALS,” Prog. Electromagn. Res., vol. 51, pp. 139–
152, 2005.
[69] J. M. Pitarke, V. M. Silkin, E. V Chulkov, and P. M. Echenique, “Theory of
surface plasmons and surface-plasmon polaritons,” Reports Prog. Phys., vol. 70,
no. 1, pp. 1–87, Jan. 2007.
[70] S. Efrima and H. Metiu, “Classical theory of light scattering by an adsorbed
molecule. I. Theory,” J. Chem. Phys., vol. 70, no. 4, p. 1602, Jul. 1979.
[71] P. K. Aravind and H. Metiu, “The enhancement of raman and fluorescent intensity
by small surface roughness. changes in dipole emission,” Chem. Phys. Lett., vol.
74, no. 2, pp. 301–305, Sep. 1980.
[72] M. Mirkin, CA and Ratner, “Controlled synthesis and quantum-size effect in goldcoated nanoparticles,” Annu Rev Phys Chem, vol. 101, p. 1593, 1997.
[73] J. Gersten and A. Nitzan, “Electromagnetic theory of enhanced Raman scattering
by molecules adsorbed on rough surfaces,” J. Chem. Phys., vol. 73, no. 7, p. 3023,
1980.
[74] M. A. Rampi, O. J. A. Schueller, and G. M. Whitesides, “Alkanethiol selfassembled monolayers as the dielectric of capacitors with nanoscale thickness,”
Appl. Phys. Lett., vol. 72, no. 14, p. 1781, Apr. 1998.
[75] D.-S. Wang, H. Chew, and M. Kerker, “Enhanced Raman scattering at the surface
(SERS) of a spherical particle,” Appl. Opt., vol. 19, no. 14, p. 2256, Jul. 1980.
[76] M. Brack, “The physics of simple metal clusters: self-consistent jellium model and
semiclassical approaches,” Rev. Mod. Phys., vol. 65, no. 3, pp. 677–732, Jul. 1993.
[77] A. Adams, R. W. Rendell, R. W. Garnett, P. K. Hansma, and H. Metiu, “Effect of
metal film thickness on surface-atom coupling,” Opt. Commun., vol. 34, no. 3, pp.
417–420, Sep. 1980.
[78] A. Adams, R. W. Rendell, W. P. West, H. P. Broida, P. K. Hansma, and H. Metiu,
“Luminescence and nonradiative energy transfer to surfaces,” Phys. Rev. B, vol.
21, no. 12, pp. 5565–5571, Jun. 1980.
[79] A. Wokaun, J. P. Gordon, and P. F. Liao, “Radiation Damping in SurfaceEnhanced Raman Scattering,” Phys. Rev. Lett., vol. 48, no. 14, pp. 957–960, Apr.
1982.
124
[80] L. Genzel, T. P. Martin, and U. Kreibig, “Dielectric function and plasma
resonances of small metal particles,” Zeitschrift f�r Phys. B Condens. Matter
Quanta, vol. 21, no. 4, pp. 339–346, Dec. 1975.
[81] C. C. Lam, P. T. Leung, and K. Young, “Explicit asymptotic formulas for the
positions, widths, and strengths of resonances in Mie scattering,” J. Opt. Soc. Am.
B, vol. 9, no. 9, p. 1585, Sep. 1992.
[82] M. Meier and A. Wokaun, “Enhanced fields on large metal particles: dynamic
depolarization,” Opt. Lett., vol. 8, no. 11, p. 581, Nov. 1983.
[83] U. Kreibig and C. v. Fragstein, “The limitation of electron mean free path in small
silver particles,” Zeitschrift f�r Phys., vol. 224, no. 4, pp. 307–323, Aug. 1969.
[84] R. H. Doremus and P. Rao, “Optical properties of nanosized gold particles,” J.
Mater. Res., vol. 11, no. 11, pp. 2834–2840, Jan. 2011.
[85] “Special issue: Nanostructured Materials,” Chem. Mater., vol. 8, p. 1569, 1996.
[86] J. R. and others Heath, “The chemistry of size and order on the nanometer scale,”
Sci. YORK THEN Washingt., vol. 270, p. 1315, 1995.
[87] J. J. Storhoff, R. Elghanian, R. C. Mucic, C. A. Mirkin, and R. L. Letsinger, “OnePot Colorimetric Differentiation of Polynucleotides with Single Base
Imperfections Using Gold Nanoparticle Probes,” J. Am. Chem. Soc., vol. 120, no.
9, pp. 1959–1964, Mar. 1998.
[88] M. Duval Malinsky, K. L. Kelly, G. C. Schatz, and R. P. Van Duyne, “Nanosphere
Lithography: Effect of Substrate on the Localized Surface Plasmon Resonance
Spectrum of Silver Nanoparticles,” J. Phys. Chem. B, vol. 105, no. 12, pp. 2343–
2350, Mar. 2001.
[89] R. P. Van Duyne, J. C. Hulteen, and D. A. Treichel, “Atomic force microscopy
and surface-enhanced Raman spectroscopy. I. Ag island films and Ag film over
polymer nanosphere surfaces supported on glass,” J. Chem. Phys., vol. 99, no. 3, p.
2101, Aug. 1993.
[90] U. Kreibig, M. Gartz, and A. Hilger, “Mie resonances: Sensors for physical and
chemical cluster interface properties,” Berichte der Bunsengesellschaft für Phys.
Chemie, vol. 101, no. 11, pp. 1593–1604, Nov. 1997.
[91] R. Elghanian, “Selective Colorimetric Detection of Polynucleotides Based on the
Distance-Dependent Optical Properties of Gold Nanoparticles,” Science (80-. ).,
vol. 277, no. 5329, pp. 1078–1081, Aug. 1997.
[92] A. Otto, “Raman scattering from adsorbates on silver,” Surf. Sci., vol. 92, no. 1,
pp. 145–152, Feb. 1980.
[93] R. Dornhaus, R. E. Benner, R. K. Chang, and I. Chabay, “Surface plasmon
125
contribution to SERS,” Surf. Sci., vol. 101, no. 1–3, pp. 367–373, Dec. 1980.
[94] S. Nie, “Probing Single Molecules and Single Nanoparticles by Surface-Enhanced
Raman Scattering,” Science (80-. )., vol. 275, no. 5303, pp. 1102–1106, Feb. 1997.
[95] C. Y. Chen and E. Burstein, “Giant Raman Scattering by Molecules at MetalIsland Films,” Phys. Rev. Lett., vol. 45, no. 15, pp. 1287–1291, Oct. 1980.
[96] M. Quinten, A. Leitner, J. R. Krenn, and F. R. Aussenegg, “Electromagnetic
energy transport via linear chains of silver nanoparticles,” Opt. Lett., vol. 23, no.
17, p. 1331, Sep. 1998.
[97] S. A. Maier, P. G. Kik, and H. A. Atwater, “Optical pulse propagation in metal
nanoparticle chain waveguides,” Phys. Rev. B, vol. 67, no. 20, p. 205402, May
2003.
[98] J. R. Krenn, A. Dereux, J. C. Weeber, E. Bourillot, Y. Lacroute, J. P. Goudonnet,
G. Schider, W. Gotschy, A. Leitner, F. R. Aussenegg, and C. Girard, “Squeezing
the Optical Near-Field Zone by Plasmon Coupling of Metallic Nanoparticles,”
Phys. Rev. Lett., vol. 82, no. 12, pp. 2590–2593, Mar. 1999.
[99] J. Pendry, “APPLIED PHYSICS:Enhanced: Playing Tricks with Light,” Science
(80-. )., vol. 285, no. 5434, pp. 1687–1688, Sep. 1999.
[100] E. Betzig and J. K. Trautman, “Near-field optics: microscopy, spectroscopy, and
surface modification beyond the diffraction limit.,” Science, vol. 257, no. 5067, pp.
189–95, Jul. 1992.
[101] R. D. Grober, T. D. Harris, J. K. Trautman, E. Betzig, W. Wegscheider, L.
Pfeiffer, and K. West, “Optical spectroscopy of a GaAs/AlGaAs quantum wire
structure using near-field scanning optical microscopy,” Appl. Phys. Lett., vol. 64,
no. 11, p. 1421, Mar. 1994.
[102] S. K. Buratto, J. W. P. Hsu, J. K. Trautman, E. Betzig, R. B. Bylsma, C. C. Bahr,
and M. J. Cardillo, “Imaging InGaAsP quantum-well lasers using near-field
scanning optical microscopy,” J. Appl. Phys., vol. 76, no. 12, p. 7720, Dec. 1994.
[103] J. I. Gersten, “The effect of surface roughness on surface enhanced Raman
scattering,” J. Chem. Phys., vol. 72, no. 10, p. 5779, 1980.
[104] M. Moskovits, “Surface roughness and the enhanced intensity of Raman scattering
by molecules adsorbed on metals,” J. Chem. Phys., vol. 69, no. 9, p. 4159, 1978.
[105] M. Moskovits, “Enhanced Raman scattering by molecules adsorbed on electrodes-a theoretical model,” Solid State Commun., vol. 32, no. 1, pp. 59–62, Oct. 1979.
[106] M. Kerker, D.-S. Wang, and H. Chew, “Surface enhanced Raman scattering
(SERS) by molecules adsorbed at spherical particles: errata,” Appl. Opt., vol. 19,
no. 24, p. 4159, Dec. 1980.
126
[107] B. PETTINGER, G. PICARDI, R. SCHUSTER, and G. ERTL, “Surface Enhanced
Raman Spectroscopy : Towards Single Molecule Spectroscopy,” Electrochemistry,
vol. 68, no. 12, p. 942, 2000.
[108] V. Bonacic-Koutecky, P. Fantucci, and J. Koutecky, “Quantum chemistry of small
clusters of elements of groups Ia, Ib, and IIa: fundamental concepts, predictions,
and interpretation of experiments,” Chem. Rev., vol. 91, no. 5, pp. 1035–1108, Jul.
1991.
[109] K.-P. Charlé, F. Frank, and W. Schulze, “The Optical Properties of Silver
Microcrystallites in Dependence on Size and the Influence of the Matrix
Environment,” Berichte der Bunsengesellschaft für Phys. Chemie, vol. 88, no. 4,
pp. 350–354, Apr. 1984.
[110] J. A. A. J. Perenboom, P. Wyder, and F. Meier, “Electronic properties of small
metallic particles,” Phys. Rep., vol. 78, no. 2, pp. 173–292, Nov. 1981.
[111] T. G. Schaaff, M. N. Shafigullin, J. T. Khoury, I. Vezmar, R. L. Whetten, W. G.
Cullen, P. N. First, C. Gutiérrez-Wing, J. Ascensio, and M. J. Jose-Yacamán,
“Isolation of Smaller Nanocrystal Au Molecules: Robust Quantum Effects in
Optical Spectra,” J. Phys. Chem. B, vol. 101, no. 40, pp. 7885–7891, Oct. 1997.
[112] B. M. I. van der Zande, M. R. Böhmer, L. G. J. Fokkink, and C. Schönenberger,
“Aqueous Gold Sols of Rod-Shaped Particles,” J. Phys. Chem. B, vol. 101, no. 6,
pp. 852–854, Feb. 1997.
[113] T. G. Schaaff, G. Knight, M. N. Shafigullin, R. F. Borkman, and R. L. Whetten,
“Isolation and Selected Properties of a 10.4 kDa Gold:Glutathione Cluster
Compound,” J. Phys. Chem. B, vol. 102, no. 52, pp. 10643–10646, Dec. 1998.
[114] A. J. Nozik and R. Memming, “Physical Chemistry of Semiconductor−Liquid
Interfaces,” J. Phys. Chem., vol. 100, no. 31, pp. 13061–13078, Jan. 1996.
[115] S. Link, M. B. Mohamed, and M. A. El-Sayed, “Simulation of the Optical
Absorption Spectra of Gold Nanorods as a Function of Their Aspect Ratio and the
Effect of the Medium Dielectric Constant,” J. Phys. Chem. B, vol. 103, no. 16, pp.
3073–3077, 1999.
[116] Yu, S.-S. Chang, C.-L. Lee, and C. R. C. Wang, “Gold Nanorods: Electrochemical
Synthesis and Optical Properties,” J. Phys. Chem. B, vol. 101, no. 34, pp. 6661–
6664, Aug. 1997.
[117] K. L. Kelly, E. Coronado, L. L. Zhao, and G. C. Schatz, “The Optical Properties of
Metal Nanoparticles: The Influence of Size, Shape, and Dielectric Environment,”
J. Phys. Chem. B, vol. 107, no. 3, pp. 668–677, Jan. 2003.
[118] R. P. Devaty and A. J. Sievers, “Possibility of observing quantum size effects in
127
the electromagnetic absorption spectrum of small metal particles,” Phys. Rev. B,
vol. 32, no. 4, pp. 1951–1954, Aug. 1985.
[119] M. Kubo and S. Nakamura, “The Dielectric Constant of Dispersion of Spherical
Particles,” Bull. Chem. Soc. Jpn., vol. 26, no. 6, pp. 318–322, 1953.
[120] T. Maniv and H. Metiu, “Electrodynamics at a metal surface with applications to
the spectroscopy of adsorbed molecules. I. General theory,” Phys. Rev. B, vol. 22,
no. 10, pp. 4731–4738, Nov. 1980.
[121] G. C. Papavassiliou, “Optical properties of small inorganic and organic metal
particles,” Prog. Solid State Chem., vol. 12, no. 3–4, pp. 185–271, Jan. 1979.
[122] P. K. Aravind, A. Nitzan, and H. Metiu, “The interaction between electromagnetic
resonances and its role in spectroscopic studies of molecules adsorbed on colloidal
particles or metal spheres,” Surf. Sci., vol. 110, no. 1, pp. 189–204, Sep. 1981.
[123] M. Quinten and U. Kreibig, “Absorption and elastic scattering of light by particle
aggregates,” Appl. Opt., vol. 32, no. 30, p. 6173, Oct. 1993.
[124] M. Quinten and U. Kreibig, “Optical properties of aggregates of small metal
particles,” Surf. Sci., vol. 172, no. 3, pp. 557–577, Jul. 1986.
[125] J. C. Maxwell Garnett, “Colours in Metal Glasses and in Metallic Films.II,”
proceeding R. Soc. London, vol. 73, pp. 443–445, 1904.
[126] J. C. M. Garnett, “Colours in Metal Glasses, in Metallic Films, and in Metallic
Solutions. II,” Philos. Trans. R. Soc. A Math. Phys. Eng. Sci., vol. 205, no. 387–
401, pp. 237–288, 1906.
[127] C. A. Foss, G. L. Hornyak, J. A. Stockert, and C. R. Martin, “Optical properties of
composite membranes containing arrays of nanoscopic gold cylinders,” J. Phys.
Chem., vol. 96, no. 19, pp. 7497–7499, Sep. 1992.
[128] G. L. Hornyak, C. J. Patrissi, and C. R. Martin, “Fabrication, Characterization, and
Optical Properties of Gold Nanoparticle/Porous Alumina Composites: The
Nonscattering Maxwell−Garnett Limit,” J. Phys. Chem. B, vol. 101, no. 9, pp.
1548–1555, Feb. 1997.
[129] J. Belloni, M. Mostafavi, H. Remita, J.-L. Marignier, and and M.-O. Delcourt,
“Radiation-induced synthesis of mono- and multi-metallic clusters and
nanocolloids,” New Journal of Chemistry, vol. 22. pp. 1239–1255, 1998.
[130] G. C. Schatz, “Electrodynamics of nonspherical noble metal nanoparticles and
nanoparticle aggregates,” J. Mol. Struct. THEOCHEM, vol. 573, no. 1–3, pp. 73–
80, Oct. 2001.
[131] P. W. Barber and S. C. Hill, Light Scattering by Particles: Computational
Methods. World Scientific, 1990.
128
[132] B. T. Draine and P. J. Flatau, “Discrete-dipole approximation for scattering
calculations,” J. Opt. Soc. Am. A, vol. 11, no. 4, p. 1491, Apr. 1994.
[133] M. M. Miller and A. A. Lazarides, “Sensitivity of metal nanoparticle surface
plasmon resonance to the dielectric environment,” J. Phys. Chem. B., vol. 109, no.
46, pp. 21556–21565, 2005.
[134] C. R. Purcell, Edward M and Pennypacker, “Scattering and absorption of light by
nonspherical dielectric grains,” Astrophys. J., vol. 186, pp. 705–714, 1973.
[135] T. R. Jensen, M. L. Duval, K. L. Kelly, A. A. Lazarides, G. C. Schatz, and R. P.
Van Duyne, “Nanosphere Lithography: Effect of the External Dielectric Medium
on the Surface Plasmon Resonance Spectrum of a Periodic Array of Silver
Nanoparticles,” J. Phys. Chem. B, vol. 103, no. 45, pp. 9846–9853, Nov. 1999.
[136] K. Yee, “Numerical solution of initial boundary value problems involving
Maxwell’s equations in isotropic media,” Antennas and Propagation, IEEE
Transactions on, vol. 14, no. 3. pp. 302–307, 1966.
[137] A. Taflove, “Application of the Finite-Difference Time-Domain Method to
Sinusoidal Steady-State Electromagnetic-Penetration Problems,” IEEE Trans.
Electromagn. Compat., vol. EMC-22, no. 3, pp. 191–202, Aug. 1980.
[138] Optiwave, “OptiFDTD,” 2012.
[139] J. a. Pereda, A. Grande, O. González, and Á. Vegas, “The 1D ADI-FDTD method
in lossy media,” IEEE Antennas Wirel. Propag. Lett., vol. 7, no. FEBRUARY, pp.
477–480, 2008.
[140] D. M. Sullivan, Electromagnetic Simulation Using the FDTD Method. John Wiley
& Sons, 2013.
[141] J. B. Schneider, “Understanding the Finite-Difference Time-Domain Method,” Self
Publ., 2013.
[142] R. Jin, Y. Cao, C. a Mirkin, K. L. Kelly, G. C. Schatz, and J. G. Zheng,
“Photoinduced conversion of silver nanospheres to nanoprisms.,” Science, vol.
294, no. 5548, pp. 1901–1903, 2001.
[143] B. O. Dabbousi, J. Rodriguez, F. V Mikulec, J. R. Heine, H. Mattoussi, R. Ober,
K. F. Jensen, and M. G. Bawendi, “(CdSe)ZnS Core - Shell Quantum Dots :
Synthesis and Characterization of a Size Series of Highly Luminescent
Nanocrystallites,” J. Phys. Chem. B, vol. 101, no. 97, pp. 9463–9475, 1997.
[144] A. P. Alivisatos, “Perspectives on the Physical Chemistry of Semiconductor
Nanocrystals,” J. Phys. Chem., vol. 100, no. 31, pp. 13226–13239, Jan. 1996.
[145] C. B. Murray, D. J. Norris, and M. G. Bawendi, “Synthesis and characterization of
nearly monodisperse CdE (E = sulfur, selenium, tellurium) semiconductor
129
nanocrystallites,” J. Am. Chem. Soc., vol. 115, no. 19, pp. 8706–8715, Sep. 1993.
[146] A. C. Templeton, J. J. Pietron, R. W. Murray, P. Mulvaney, K. Laboratories, V.
Uni, C. Hill, and N. Carolina, “Solvent Refractive Index and Core Charge
Influences on the Surface Plasmon Absorbance of Alkanethiolate MonolayerProtected Gold Clusters,” J. Phys. Chem. B, vol. 104, no. 3, pp. 564–570, 2000.
[147] M. Gao, S. Kirstein, H. Möhwald, A. L. Rogach, A. Kornowski, A. Eychmüller,
and H. Weller, “Strongly Photoluminescent CdTe Nanocrystals by Proper Surface
Modification,” J. Phys. Chem. B, vol. 102, no. 43, pp. 8360–8363, Oct. 1998.
[148] X. Peng, M. C. Schlamp, A. V. Kadavanich, and A. P. Alivisatos, “Epitaxial
Growth of Highly Luminescent CdSe/CdS Core/Shell Nanocrystals with
Photostability and Electronic Accessibility,” J. Am. Chem. Soc., vol. 119, no. 30,
pp. 7019–7029, Jul. 1997.
[149] S.-M. Lee, Y. Jun, S.-N. Cho, and J. Cheon, “Single-Crystalline Star-Shaped
Nanocrystals and Their Evolution: Programming the Geometry of Nano-Building
Blocks,” J. Am. Chem. Soc., vol. 124, no. 38, pp. 11244–11245, Sep. 2002.
[150] S. Chen, Z. L. Wang, J. Ballato, S. H. Foulger, and D. L. Carroll, “Monopod,
Bipod, Tripod, and Tetrapod Gold Nanocrystals,” J. Am. Chem. Soc., vol. 125, no.
52, pp. 16186–16187, Dec. 2003.
[151] E. Hao, R. C. Bailey, G. C. Schatz, J. T. Hupp, and S. Li, “Synthesis and Optical
Properties of ‘Branched’ Gold Nanocrystals,” Nano Lett., vol. 4, no. 2, pp. 327–
330, Feb. 2004.
[152] L. Manna, E. C. Scher, and A. P. Alivisatos, “Synthesis of Soluble and Processable
Rod-, Arrow-, Teardrop-, and Tetrapod-Shaped CdSe Nanocrystals,” J. Am. Chem.
Soc., vol. 122, no. 51, pp. 12700–12706, Dec. 2000.
[153] L. Manna, D. J. Milliron, A. Meisel, E. C. Scher, and A. P. Alivisatos, “Controlled
growth of tetrapod-branched inorganic nanocrystals,” Nat. Mater., vol. 2, no. 6, pp.
382–385, Jun. 2003.
[154] Y. Jin and S. Dong, “One-Pot Synthesis and Characterization of Novel
Silver−Gold Bimetallic Nanostructures with Hollow Interiors and Bearing
Nanospikes,” J. Phys. Chem. B, vol. 107, no. 47, pp. 12902–12905, Nov. 2003.
[155] S. . Oldenburg, R. . Averitt, S. . Westcott, and N. . Halas, “Nanoengineering of
optical resonances,” Chem. Phys. Lett., vol. 288, no. 2–4, pp. 243–247, May 1998.
[156] S. J. Oldenburg, J. B. Jackson, S. L. Westcott, and N. J. Halas, “Infrared extinction
properties of gold nanoshells,” Appl. Phys. Lett., vol. 75, no. 19, p. 2897, 1999.
[157] C. Graf and A. van Blaaderen, “Metallodielectric Colloidal Core−Shell Particles
for Photonic Applications,” Langmuir, vol. 18, no. 2, pp. 524–534, Jan. 2002.
130
[158] J. B. Jackson and N. J. Halas, “Silver Nanoshells: Variations in Morphologies and
Optical Properties,” J. Phys. Chem. B, vol. 105, no. 14, pp. 2743–2746, Apr. 2001.
[159] V. F. Puntes, D. Zanchet, C. K. Erdonmez, and A. P. Alivisatos, “Synthesis of hcpCo Nanodisks,” J. Am. Chem. Soc., vol. 124, no. 43, pp. 12874–12880, Oct. 2002.
[160] S. Chen, Z. Fan, and D. L. Carroll, “Silver Nanodisks: Synthesis, Characterization,
and Self-Assembly,” J. Phys. Chem. B, vol. 106, no. 42, pp. 10777–10781, Oct.
2002.
[161] M.-P. and others Maillard, Mathieu and Giorgio, Suzanne and Pileni, “Silver
nanodisks,” Adv. Mater., vol. 14, no. 15, p. 1084, 2002.
[162] I. Pastoriza-Santos and L. M. Liz-Marzán, “Synthesis of Silver Nanoprisms in
DMF,” Nano Lett., vol. 2, no. 8, pp. 903–905, Aug. 2002.
[163] J. Yang and J. H. Fendler, “Morphology Control of PbS Nanocrystallites,
Epitaxially Grown under Mixed Monolayers,” J. Phys. Chem., vol. 99, no. 15, pp.
5505–5511, Apr. 1995.
[164] Y. Sun, B. Mayers, and Y. Xia, “Transformation of Silver Nanospheres into
Nanobelts and Triangular Nanoplates through a Thermal Process,” Nano Lett., vol.
3, no. 5, pp. 675–679, May 2003.
[165] Y. Xia, P. Yang, Y. Sun, Y. Wu, B. Mayers, B. Gates, Y. Yin, F. Kim, and H. Yan,
“One-Dimensional Nanostructures: Synthesis, Characterization, and Applications,”
Adv. Mater., vol. 15, no. 5, pp. 353–389, Mar. 2003.
[166] B. D. Busbee, S. O. Obare, and C. J. Murphy, “An Improved Synthesis of HighAspect-Ratio Gold Nanorods,” Adv. Mater., vol. 15, no. 5, pp. 414–416, Mar.
2003.
[167] S.-S. Chang, C.-W. Shih, C.-D. Chen, W.-C. Lai, and C. R. C. Wang, “The Shape
Transition of Gold Nanorods,” Langmuir, vol. 15, no. 3, pp. 701–709, Feb. 1999.
[168] N. R. Jana, L. Gearheart, and C. J. Murphy, “Wet chemical synthesis of silver
nanorods and nanowires of controllable aspect ratio,” Chem. Commun., no. 7, pp.
617–618, 2001.
[169] F. Kim, J. H. Song, and P. Yang, “Photochemical synthesis of gold nanorods.,” J.
Am. Chem. Soc., vol. 124, no. 48, pp. 14316–7, Dec. 2002.
[170] Y. Sun, “Shape-Controlled Synthesis of Gold and Silver Nanoparticles,” Science
(80-. )., vol. 298, no. 5601, pp. 2176–2179, Dec. 2002.
[171] M. A. Ahmadi, Temer S and Wang, Zhong L and Green, Travis C and Henglein,
Arnim and El-Sayed, “Shape-controlled synthesis of colloidal platinum
nanoparticles,” Science (80-. )., vol. 272, no. 5270, p. 1924, 1996.
131
[172] X. Peng, L. Manna, W. Yang, J. Wickham, E. Scher, A. Kadavanich, and A. P.
Alivisatos, “Shape control of CdSe nanocrystals,” Nature, vol. 404, no. 6773, pp.
59–61, Mar. 2000.
[173] M. B. Mohamed, V. Volkov, S. Link, and M. A. El-Sayed, “The `lightning’ gold
nanorods: fluorescence enhancement of over a million compared to the gold
metal,” Chem. Phys. Lett., vol. 317, no. 6, pp. 517–523, Feb. 2000.
[174] W. U. Huynh and A. P. A. Janke J. Dittmer, “Hybrid Nanorod-Polymer Solar
Cells,” Science (80-. )., vol. 295, no. 5564, pp. 2425–2427, Mar. 2002.
[175] Y. Sun and Y. Xia, “Increased Sensitivity of Surface Plasmon Resonance of Gold
Nanoshells Compared to That of Gold Solid Colloids in Response to
Environmental Changes,” Anal. Chem., vol. 74, no. 20, pp. 5297–5305, Oct. 2002.
[176] E. Hao and G. C. Schatz, “Electromagnetic fields around silver nanoparticles and
dimers,” J. Chem. Phys., vol. 120, no. 1, p. 357, 2004.
[177] B. Nikoobakht, J. Wang, and M. A. El-Sayed, “Surface-enhanced Raman
scattering of molecules adsorbed on gold nanorods: off-surface plasmon resonance
condition,” Chem. Phys. Lett., vol. 366, no. 1–2, pp. 17–23, Nov. 2002.
[178] G. S. Métraux, Y. C. Cao, R. Jin, and C. a. Mirkin, “Triangular Nanoframes Made
of Gold and Silver,” Nano Lett., vol. 3, no. 4, pp. 519–522, Apr. 2003.
[179] Y. Sun and Y. Xia, “Triangular Nanoplates of Silver: Synthesis, Characterization,
and Use as Sacrificial Templates For Generating Triangular Nanorings of Gold,”
Adv. Mater., vol. 15, no. 9, pp. 695–699, May 2003.
[180] P. D. Cozzoli, A. Kornowski, and H. Weller, “Low-temperature synthesis of
soluble and processable organic-capped anatase TiO2 nanorods.,” J. Am. Chem.
Soc., vol. 125, no. 47, pp. 14539–48, Nov. 2003.
[181] S.-J. Park, S. Kim, S. Lee, Z. G. Khim, K. Char, and T. Hyeon, “Synthesis and
Magnetic Studies of Uniform Iron Nanorods and Nanospheres,” J. Am. Chem.
Soc., vol. 122, no. 35, pp. 8581–8582, Sep. 2000.
[182] A. Gole and C. J. Murphy, “Polyelectrolyte-coated gold nanorods: Synthesis,
characterization and immobilization,” Chem. Mater., vol. 17, no. 6, pp. 1325–
1330, Mar. 2005.
[183] M. D. Malinsky, K. L. Kelly, G. C. Schatz, and R. P. Van Duyne, “Chain Length
Dependence and Sensing Capabilities of the Localized Surface Plasmon
Resonance of Silver Nanoparticles Chemically Modified with Alkanethiol SelfAssembled Monolayers,” J. Am. Chem. Soc., vol. 123, no. 7, pp. 1471–1482, Feb.
2001.
[184] A. J. Haes and R. P. Van Duyne, “A Nanoscale Optical Biosensor: Sensitivity and
132
Selectivity of an Approach Based on the Localized Surface Plasmon Resonance
Spectroscopy of Triangular Silver Nanoparticles,” J. Am. Chem. Soc., vol. 124, no.
35, pp. 10596–10604, Sep. 2002.
[185] G. Chumanov, K. Sokolov, B. W. Gregory, and T. M. Cotton, “Colloidal metal
films as a substrate for surface-enhanced spectroscopy,” J. Phys. Chem., vol. 99,
no. 23, pp. 9466–9471, Jun. 1995.
[186] C. L. Haynes and R. P. Van Duyne, “Nanosphere lithography: A versatile
nanofabrication tool for studies of size-dependent nanoparticle optics,” J. Phys.
Chem. B, vol. 105, no. 24, pp. 5599–5611, 2001.
[187] C. Xue, Z. Li, and C. A. Mirkin, “Large-scale assembly of single-crystal silver
nanoprism monolayers.,” Small, vol. 1, no. 5, pp. 513–6, May 2005.
[188] H. S. Nalwa, Nanostructured Materials and Nanotechnology: Concise Edition,
Gulf Profe. Gulf Professional Publishing, 2001.
[189] N. Malikova, I. Pastoriza-santos, M. Schierhorn, N. A. Kotov, and L. M. Lizmarza, “Layer-by-Layer Assembled Mixed Spherical and Planar Gold
Nanoparticles : Control of Interparticle Interactions,” Langmuir, vol. 18, no. 9, pp.
3694–3697, 2002.
[190] T. J. Norman, C. D. Grant, D. Magana, J. Z. Zhang, D. Cao, F. Bridges, and A.
Van Buuren, “Near Infrared Optical Absorption of Gold Nanoparticle
Aggregates,” J. Phys. Chem. B, vol. 106, no. 28, pp. 7005–7012, 2002.
[191] C. S. Ah, Y. J. Yun, H. J. Park, W. Kim, D. H. Ha, and W. S. Yun, “SizeControlled Synthesis of Machinable Single Crystalline Gold Nanoplates,” Chem.
Mater., vol. 17, no. 22, pp. 5558–5561, 2005.
[192] J. E. Millstone, S. Park, K. L. Shuford, L. Qin, G. C. Schatz, and C. a. Mirkin,
“Observation of a quadrupole plasmon mode for a colloidal solution of gold
nanoprisms,” J. Am. Chem. Soc., vol. 127, no. 15, pp. 5312–5313, 2005.
[193] S. Chen and D. L. Carroll, “Synthesis and Characterization of Truncated
Triangular Silver Nanoplates,” Nano Lett., vol. 2, no. 9, pp. 1003–1007, Sep. 2002.
[194] S. Chen and D. L. Carroll, “Silver Nanoplates: Size Control in Two Dimensions
and Formation Mechanisms,” J. Phys. Chem. B, vol. 108, no. 18, pp. 5500–5506,
May 2004.
[195] G. S. Métraux and C. a. Mirkin, “Rapid Thermal Synthesis of Silver Nanoprisms
with Chemically Tailorable Thickness **,” Adv. Mater., vol. 17, no. 4, pp. 412–
415, 2005.
[196] T. Klaus, R. Joerger, E. Olsson, and C.-G. Granqvist, “Silver-based crystalline
nanoparticles, microbially fabricated,” Proc. Natl. Acad. Sci., vol. 96, no. 24, pp.
133
13611–13614, 1999.
[197] B. Liu, J. Xie, J. Y. Lee, Y. P. Ting, and J. P. Chen, “Optimization of High-Yield
Biological Synthesis of Single-Crystalline Gold Nanoplates,” J. Phys. Chem. B,
vol. 109, no. 32, pp. 15256–15263, 2005.
[198] S. S. Shankar, A. Rai, B. Ankamwar, A. Singh, A. Ahmad, and M. Sastry,
“Biological synthesis of triangular gold nanoprisms,” Nat. Mater., vol. 3, no. 7, pp.
482–488, Jul. 2004.
[199] S. P. Chandran, M. Chaudhary, R. Pasricha, A. Ahmad, and M. Sastry, “Synthesis
of gold nanotriangles and silver nanoparticles using Aloe vera plant extract.,”
Biotechnol. Prog., vol. 22, no. 2, pp. 577–83, Jan. .
[200] S. Brown, M. Sarikaya, and E. Johnson, “A Genetic Analysis of Crystal Growth,”
J. Mol. Biol., vol. 299, pp. 725–735, 2000.
[201] L. Jiang, S. Xu, J. Zhu, J. Zhang, J. Zhu, and H. Chen, “Ultrasonic-Assisted
Synthesis of Monodisperse Single-Crystalline Silver Nanoplates and Gold
Nanorings,” Inorg. Chem., vol. 43, no. 19, pp. 5877–5883, 2004.
[202] Y. Y. K. Okitsu, A. Yue, S. Tanabe, H. Matsumoto, “Formation of Colloidal Gold
Nanoparticles in an Ultrasonic Field: Control of Rate of Gold(III) Reduction and
Size of Formed Gold Particles,” Langmuir, vol. 23, p. 13244, 2007.
[203] K. Okitsu, A. Yue, S. Tanabe, H. Matsumoto, and Y. Yobiko, “Formation of
Colloidal Gold Nanoparticles in an Ultrasonic Field : Control of Rate of Gold ( III
) Reduction and Size of Formed Gold Particles,” Langmuir, vol. 17, no. 25, pp.
7717–7720, 2001.
[204] M. Tsuji, M. Hashimoto, Y. Nishizawa, and T. Tsuji, “Preparation of Gold
Nanoplates by a Microwave-polyol Method,” Chem. Lett., vol. 32, no. 12, pp.
1114–1115, 2003.
[205] C. Li, W. Cai, Y. Li, J. Hu, and P. Liu, “Ultrasonically Induced Au Nanoprisms
and Their Size Manipulation Based on Aging,” J. Phys. Chem. B, vol. 110, pp.
1546–1552, 2006.
[206] I. Pastoriza-santos and L. M. Liz-marza, “Formation of PVP-Protected Metal
Nanoparticles in DMF,” Langmuir, vol. 18, no. 7, pp. 2888–2894, 2002.
[207] A. Sarkar, S. Kapoor, and T. Mukherjee, “Synthesis of silver nanoprisms in
formamide,” J. Colloid Interface Sci., vol. 287, pp. 496–500, 2005.
[208] V. Bastys, I. Pastoriza-Santos, B. Rodíguez-González, R. Vaisnoras, and L. M.
Liz-Marzán, “Formation of silver nanoprisms with surface plasmons at
communication wavelengths,” Adv. Funct. Mater., vol. 16, no. 6, pp. 766–773,
2006.
134
[209] A. Callegari, D. Tonti, and M. Chergui, “Photochemically Grown Silver
Nanoparticles with Wavelength-Controlled Size and Shape,” Nano Lett., vol. 3, pp.
1565–1568, 2003.
[210] C. Xue, G. S. Metraux, J. E. Millstone, and C. A. Mirkin, “Mechanistic study of
photomediated triangular silver nanoprism growth,” J. Am. Chem. Soc., vol. 130,
no. 26, pp. 8337–8344, 2008.
[211] X. Wu, P. L. Redmond, H. Liu, Y. Chen, M. Steigerwald, and L. Brus,
“Photovoltage mechanism for room light conversion of citrate stabilized silver
nanocrystal seeds to large nanoprisms,” J. Am. Chem. Soc., vol. 130, pp. 9500–
9506, 2008.
[212] M. Maillard, P. Huang, and L. Brus, “Silver Nanodisk Growth by Surface Plasmon
Enhanced Photoreduction of Adsorbed [Ag +],” Nano Lett., vol. 3, no. 11, pp.
1611–1615, 2003.
[213] P. L. Redmond, E. C. Walter, and L. E. Brus, “Photoinduced thermal copper
reduction onto gold nanocrystals under potentiostatic control,” J. Phys. Chem. B,
vol. 110, no. 50, pp. 25158–25162, 2006.
[214] a J. Hallock, P. L. Redmond, and L. E. Brus, “Optical forces between metallic
particles.,” Proc. Natl. Acad. Sci. U. S. A., vol. 102, pp. 1280–1284, 2005.
[215] V. Wong and M. A. Ratner, “Size dependence of gradient and nongradient optical
forces in silver nanoparticles,” J. Opt. Soc. Am. B, vol. 24, no. 1, p. 106, 2007.
[216] A. Henglein, “Physicochemical properties of small metal particles in solution:
‘microelectrode’ reactions, chemisorption, composite metal particles, and the
atom-to-metal transition,” J. Phys. Chem., vol. 97, no. 21, pp. 5457–5471, May
1993.
[217] A. Machulek Junior, H. P. M. de Oliveira, and M. H. Gehlen, “Preparation of
silver nanoprisms using poly(N-vinyl-2-pyrrolidone) as a colloid-stabilizing agent
and the effect of silver nanoparticles on the photophysical properties of cationic
dyes.,” Photochem. Photobiol. Sci., vol. 2, pp. 921–925, 2003.
[218] C.-M. Ho, C.-K. Wong, S. K.-W. Yau, C.-N. Lok, and C.-M. Che, “Oxidative
dissolution of silver nanoparticles by dioxygen: a kinetic and mechanistic study.,”
Chem. Asian J., vol. 6, no. 9, pp. 2506–11, Sep. 2011.
[219] R. Jin, Y. Charles Cao, E. Hao, G. S. Métraux, G. C. Schatz, and C. a Mirkin,
“Controlling anisotropic nanoparticle growth through plasmon excitation,” Nature,
vol. 425, no. 6957, pp. 487–490, Oct. 2003.
[220] J. Zhang, M. R. Langille, and C. A. Mirkin, “Photomediated synthesis of silver
triangular bipyramids and prisms: the effect of pH and BSPP.,” J. Am. Chem. Soc.,
135
vol. 132, no. 35, pp. 12502–10, Sep. 2010.
[221] C. Xue, J. E. Millstone, S. Li, and C. A. Mirkin, “Plasmon-Driven Synthesis of
Triangular Core–Shell Nanoprisms from Gold Seeds,” Angew. Chemie, vol. 119,
no. 44, pp. 8588–8591, Nov. 2007.
[222] C. Xue and C. A. Mirkin, “pH-Switchable Silver Nanoprism Growth Pathways,”
Angew. Chemie, vol. 119, no. 12, pp. 2082–2084, Mar. 2007.
[223] X. Zheng, W. Xu, C. Corredor, S. Xu, J. An, B. Zhao, and J. R. Lombardi, “Laserinduced growth of monodisperse silver nanoparticles with tunable surface plasmon
resonance properties and a wavelength self-limiting effect,” J. Phys. Chem. C, vol.
111, no. 41, pp. 14962–14967, 2007.
[224] T. C. R. Rocha, H. Winnischofer, E. Westphal, and D. Zanchet, “Formation
kinetics of silver triangular nanoplates,” J. Phys. Chem. C, vol. 111, no. 7, pp.
2885–2891, 2007.
[225] A. Dmitriev, T. Pakizeh, M. Käll, and D. S. Sutherland, “Gold-silica-gold
nanosandwiches: tunable bimodal plasmonic resonators.,” Small, vol. 3, no. 2, pp.
294–9, Feb. 2007.
[226] S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J.-Y. Laluet, and T. W. Ebbesen,
“Channel plasmon subwavelength waveguide components including
interferometers and ring resonators.,” Nature, vol. 440, no. 7083, pp. 508–11, Mar.
2006.
[227] J. Homola, S. S. Yee, and G. Gauglitz, “Surface plasmon resonance sensors:
review,” Sensors Actuators B Chem., vol. 54, no. 1–2, pp. 3–15, Jan. 1999.
[228] T. M. Chinowsky, L. S. Jung, and S. S. Yee, “Optimal linear data analysis for
surface plasmon resonance biosensors,” Sensors Actuators B Chem., vol. 54, no.
1–2, pp. 89–97, Jan. 1999.
[229] K. a Willets and R. P. Van Duyne, “Localized surface plasmon resonance
spectroscopy and sensing.,” Annu. Rev. Phys. Chem., vol. 58, no. October, pp.
267–97, Jan. 2007.
[230] G. H. Chan, J. Zhao, E. M. Hicks, G. C. Schatz, and R. P. Van Duyne, “Plasmonic
Properties of Copper Nanoparticles Fabricated by Nanosphere Lithography,” Nano
Lett., vol. 7, no. 7, pp. 1947–1952, Jul. 2007.
[231] E. Ringe, J. M. McMahon, K. Sohn, C. Cobley, Y. Xia, J. Huang, G. C. Schatz, L.
D. Marks, and R. P. Van Duyne, “Unraveling the Effects of Size, Composition,
and Substrate on the Localized Surface Plasmon Resonance Frequencies of Gold
and Silver Nanocubes: A Systematic Single-Particle Approach,” J. Phys. Chem. C,
vol. 114, no. 29, pp. 12511–12516, Jul. 2010.
136
[232] O. Stranik, R. Nooney, C. McDonagh, and B. D. MacCraith, “Optimization of
Nanoparticle Size for Plasmonic Enhancement of Fluorescence,” Plasmonics, vol.
2, no. 1, pp. 15–22, Dec. 2006.
[233] P. N. Njoki, I.-I. S. Lim, D. Mott, H.-Y. Park, B. Khan, S. Mishra, R. Sujakumar,
J. Luo, and C.-J. Zhong, “Size Correlation of Optical and Spectroscopic Properties
for Gold Nanoparticles,” J. Phys. Chem. C, vol. 111, no. 40, pp. 14664–14669,
Oct. 2007.
[234] R. Cui, C. Liu, J. Shen, D. Gao, J.-J. Zhu, and H.-Y. Chen, “Gold NanoparticleColloidal Carbon Nanosphere Hybrid Material: Preparation, Characterization, and
Application for an Amplified Electrochemical Immunoassay,” Adv. Funct. Mater.,
vol. 18, no. 15, pp. 2197–2204, Aug. 2008.
[235] J. Zhou, W. Wu, D. Caruntu, M. H. Yu, a. Martin, J. F. Chen, C. J. O’Connor, and
W. L. Zhou, “Synthesis of Porous Magnetic Hollow Silica Nanospheres for
Nanomedicine Application,” J. Phys. Chem. C, vol. 111, no. 47, pp. 17473–17477,
Nov. 2007.
[236] J. Perezjuste, I. Pastorizasantos, L. Lizmarzan, and P. Mulvaney, “Gold nanorods:
Synthesis, characterization and applications,” Coord. Chem. Rev., vol. 249, no.
17–18, pp. 1870–1901, Sep. 2005.
[237] J. E. Millstone, S. J. Hurst, G. S. Métraux, J. I. Cutler, and C. a. Mirkin, “Colloidal
gold and silver triangular nanoprisms,” Small, vol. 5, no. 6, pp. 646–664, 2009.
[238] M. Tréguer-Delapierre, J. Majimel, S. Mornet, E. Duguet, and S. Ravaine,
“Synthesis of non-spherical gold nanoparticles,” Gold Bull., vol. 41, no. 2, pp.
195–207, 2008.
[239] L. Liz-Marzán, “Tailoring surface plasmons through the morphology and assembly
of metal nanoparticles,” Langmuir, vol. 22, no. 1, pp. 32–41, Jan. 2006.
[240] J. Nelayah, M. Kociak, O. Stéphan, F. J. García de Abajo, M. Tencé, L. Henrard,
D. Taverna, I. Pastoriza-Santos, L. M. Liz-Marzán, and C. Colliex, “Mapping
surface plasmons on a single metallic nanoparticle,” Nat. Phys., vol. 3, no. 5, pp.
348–353, 2007.
[241] Y. Kenzo and I. Tomohiro, “Electric field enhancement of nano gap of silver
prisms,” Chinese Phys. …, vol. 24, no. 10, pp. 29–34, 2007.
[242] J. E. Millstone, G. S. Métraux, and C. A. Mirkin, “Controlling the edge length of
gold nanoprisms via a seed-mediated approach,” Adv. Funct. Mater., vol. 16, pp.
1209–1214, 2006.
[243] M. Tsuji, M. Hashimoto, Y. Nishizawa, M. Kubokawa, and T. Tsuji, “Microwaveassisted synthesis of metallic nanostructures in solution,” Chemistry - A European
137
Journal, vol. 11. pp. 440–452, 2005.
[244] B. J. Wiley, Y. Xiong, Z. Y. Li, Y. Yin, and Y. Xia, “Right bipyramids of silver: A
new shape derived from single twinned seeds,” Nano Lett., vol. 6, pp. 765–768,
2006.
[245] J. E. Millstone, W. Wei, M. R. Jones, H. Yoo, and C. A. Mirkin, “Iodide ions
control seed-mediated growth of anisotropic gold Nanoparticles,” Nano Lett., vol.
8, pp. 2526–2529, 2008.
[246] L. J. Sherry, R. Jin, C. a Mirkin, G. C. Schatz, and R. P. Van Duyne, “Localized
surface plasmon resonance spectroscopy of single silver triangular nanoprisms,”
Nano Lett., vol. 6, no. 9, pp. 2060–2065, Sep. 2006.
[247] S. Pal, Y. K. Tak, and J. M. Song, “Does the antibacterial activity of silver
nanoparticles depend on the shape of the nanoparticle? A study of the gramnegative bacterium Escherichia coli,” Appl. Environ. Microbiol., vol. 73, no. 6, pp.
1712–1720, 2007.
[248] A. A. Ashkarran and A. Bayat, “Surface plasmon resonance of metal
nanostructures as a complementary technique for microscopic size measurement,”
vol. 2, no. d, p. 1, 2013.
[249] K. Kimura, “Shape effect and quantum size effect on small metal particles,”
Zeitschrift fur Phys. D Atoms, Mol. Clust., vol. 11, no. 4, pp. 327–332, 1989.
[250] F. Hache, D. Ricard, and C. Flytzanis, “Optical nonlinearities of small metal
particles: surface-mediated resonance and quantum size effects,” J. Opt. Soc. Am.
B, vol. 3, no. 12, p. 1647, 1986.
[251] S. Alsheheri, M. Saboktakin, and M. Matin, “The effect of truncation in plasmon
resonance of metal nanoprisms,” 2015, p. 95472H.
[252] M. L. Brongersma and V. M. Shalaev, “Applied physics. The case for
plasmonics.,” Science, vol. 328, no. 5977, pp. 440–441, 2010.
[253] S. A. Maier, Plsmonic: Fundamentals and Applications. Springer Science &
Business Media, 2007.
[254] R. Gans, “Form of ultramicroscopic particles of silver.,” Ann. Phys., vol. 47, no.
10, pp. 270–284, 1915.
[255] U. Kreibig and L. Genzel, “Optical absorption u. kreibig of small metallic
particles,” Surf. Sci., vol. 156, pp. 678–700, 1985.
[256] B. N. J. Persson, “Polarizability of small spherical metal particles: influence of the
matrix environment,” Surf. Sci., vol. 281, no. 1–2, pp. 153–162, 1993.
[257] N. Nath and A. Chilkoti, “A colorimetric gold nanoparticle sensor to interrogate
138
biomolecular interactions in real time on a surface,” Anal. Chem., vol. 74, no. 3,
pp. 504–509, 2002.
[258] A. A. Lazarides, K. Lance Kelly, T. R. Jensen, and G. C. Schatz, “Optical
properties of metal nanoparticles and nanoparticle aggregates important in
biosensors,” J. Mol. Struct. THEOCHEM, vol. 529, pp. 59–63, 2000.
[259] a. J. Haes, W. P. Hall, L. Chang, W. L. Klein, and R. P. Van Duyne, “A Localized
Surface Plasmon Resonance Biosensor: First Steps toward an Assay for
Alzheimer’s Disease,” Nano Lett., vol. 4, no. 6, pp. 1029–1034, 2004.
[260] G. Raschke, S. Brogl, A. S. Susha, A. L. Rogach, T. A. Klar, J. Feldmann, B.
Fieres, N. Petkov, T. Bein, A. Nichtl, and K. Kürzinger, “Gold nanoshells improve
single nanoparticle molecular sensors,” Nano Lett., vol. 4, no. 10, pp. 1853–1857,
2004.
[261] T. R. Jensen, M. L. Duval, T. R. Jensen, M. L. Duval, K. L. Kelly, K. L. Kelly, a a
Lazarides, A. a. Lazarides, G. C. Schatz, G. C. Schatz, and R. P. Van Duyne,
“Nanosphere Lithography: Effect of the External Dielectric Medium on the
Surface Plasmon Resonance Spectrum of a Periodic Array of Silver
Nanoparticles,” J. Phys. Chem. B, vol. 103, no. 45, pp. 9846–9853, 1999.
[262] E. A. Coronado and G. C. Schatz, “Surface plasmon broadening for arbitrary shape
nanoparticles: A geometrical probability approach,” J. Chem. Phys., vol. 119, no.
7, pp. 3926–3934, 2003.
[263] F. Tam, C. Moran, and N. Halas, “Geometrical parameters controlling sensitivity
of nanoshell plasmon resonances to changes in dielectric environment,” J. Phys.
Chem. B, vol. 108, no. 45, pp. 17290–17294, 2004.
[264] S. Link, M. B. Mohamed, and M. A. El-Sayed, “Simulation of the Optical
Absorption Spectra of Gold Nanorods as a Function of Their Aspect Ratio and the
Effect of the Medium Dielectric Constant,” J. Phys. Chem. B, vol. 103, no. 16, pp.
3073–3077, Apr. 1999.
[265] K. M. Mayer, S. Lee, H. Liao, B. C. Rostro, A. Fuentes, P. T. Scully, C. L. Nehl,
and J. H. Hafner, “A Label-Free Immunoassay Based Upon Localized Surface
Plasmon Resonance of Gold Nanorods,” ACS Nano, vol. 2, no. 4, pp. 687–692,
Apr. 2008.
[266] N. Nath and A. Chilkoti, “Label-free biosensing by surface plasmon resonance of
nanoparticles on glass: Optimization of nanoparticle size,” Anal. Chem., vol. 76,
no. 18, pp. 5370–5378, 2004.
[267] J. J. Mock, D. R. Smith, and S. Schultz, “Local refractive index dependence of
plasmon resonance spectra from individual nanoparticles,” Nano Lett., vol. 3, no.
4, pp. 485–491, 2003.
139
[268] A. D. McFarland and R. P. Van Duyne, “Single silver nanoparticles as real-time
optical sensors with zeptomole sensitivity,” Nano Lett., vol. 3, no. 8, pp. 1057–
1062, 2003.
[269] M. M. Shahjamali, M. Bosman, S. Cao, X. Huang, S. Saadat, E. Martinsson, D.
Aili, Y. Y. Tay, B. Liedberg, S. C. J. Loo, H. Zhang, F. Boey, and C. Xue, “Gold
Coating of Silver Nanoprisms,” Adv. Funct. Mater., vol. 22, no. 4, pp. 849–854,
Feb. 2012.
[270] S. Alsheheri, M. Saboktakin, and M. Matin, “Hybrid plasmonic nanosandwich
structures,” 2015, p. 95442R.
[271] S. Alsheheri, M. Saboktakin, and M. Matin, “STUDY OF THE SNIP EFFECT IN
RESONANCE OF HYBRID PLASMONIC NANOSANDWICH STRUCTURES
IN OPTICAL RANGE,” Asian J. Sci. Technol., vol. 7, no. 2, pp. 2446–2454,
2016.
140
Appendix A: List of Publications
Journal Publications:
[1] S. Alsheheri, M. Saboktakin, and M. Matin, “A Simulation Study of the Plasmonic
Resonance of Sharp and Truncated Silver Triangular Nanoprisms,” J. Multidiscip. Eng.
Sci. Technol., vol. 3, no. 1, pp. 3799–3802, 2016.
[2] S. Alsheheri, M. Saboktakin, and M. Matin, “Study of the Snip Effect in Resonance
of Hybrid Plasmonic Nanosandwich Structures in Optical Range,” Asian Journal
Of Science And Technologies., February, 2016 ( In Press)
Conference Publications:
[1] S. Alsheheri, M. Saboktakin, and M. Matin, “Hybrid plasmonic nanosandwich
structures,” 2015, p. 95442R.
[2] S. Alsheheri, M. Saboktakin, and M. Matin, “The effect of truncation in plasmon
resonance of metal nanoprisms,” 2015, p. 95472H.
141
Permission Asian Journal of Science and Technology
http://journalajst.com/
Copyrights:
Open Access authors retain the copyrights of their papers, and all open access
articles are distributed under the terms of the Creative Commons Attribution
license, which permits unrestricted use, distribution and reproduction in any
medium, provided that the original work is properly cited.
142
Permission from SPIE
143
Permission from Prof. Karl Heinz at Journal of Multidisciplinary Engineering Science
144